Answer:
\(the \: horizontal \: component \: of \: the \: acceleration : \\ a_{x} = 7.21\: {m(s)}^{ - 2} \\ the \: vertical \: component \: of \: the \: acceleration : \\ a_{y} = 2.07 \: {m(s)}^{ - 2} \)
Explanation:
\(the \: horizontal \: component \: of \: the \: acceleration : \\ a_{x} = a \: \cos( \alpha ) \\ a_{x} = 7.5 \: \cos(16) \\ a_{x} = 7.2094627195 \: {m(s)}^{ - 2} \\ \\ the \: vertical \: component \: of \: the \: acceleration : \\ a_{y} = a \: \sin( \alpha )\\a_{y} = 7.5 \: \sin(16) \\ a_{y} = 2.0672801686 \: {m(s)}^{ - 2} \\ \)
Answer:
horizontal component: \(7.2\ m/s^2\)
vertical component: \(2.1\ m/s^2\)
Explanation:
Rectangular components of a vector
Given a vector as a (magnitude, angle) pair, the rectangular components can be calculated as:
\(a_x= magnitude*cos(angle)\)
\(a_y=magnitude*sin(angle)\)
The acceleration of the airplane is given with a magnitude of 7.5 m/s^2 and an angle of 16°.
Calculate the components:
\(a_x=7.5*cos(16^\circ)=7.2\ m/s^2\)
\(a_y=7.5*sin(16^\circ)=2.1\ m/s^2\)
horizontal component: \(7.2\ m/s^2\)
vertical component: \(2.1\ m/s^2\)
HELP ME ASAPPPPPPPPPPP
A penny sinks to the bottom of a wishing well
What type of frictional force is that?
The frictional force involved when a penny sinks to the bottom of a wishing well is primarily due to viscous drag or fluid friction. As the penny moves through the water, it experiences resistance from the surrounding fluid. This resistance is caused by the frictional forces between the water molecules and the penny's surface.
HELP PLEASEEEEEE HELP PLEASE
The letter that represents the various descriptions is as follows:
5.) Angle of incidence: B
6.) Object: D
7.) Plain mirror:A
8.) Reflection: E
9.) Angle of reflection: C
10.) Normal: F
How does the diagram explain the law of reflection?The law of reflection in a plain mirror states that the angle of reflection is equal to the angle of incidence.
The diagram explains the law of reflection on a plain mirror because it shows the reflection of the object D as E after creating an angle of incidence B on the plane mirror surface A which is equal to the angle of reflection C.
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what is the total moved without regard to direction
The entire motion of an object, regardless of direction.
In physics, motion is that the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of regard to an observer and measuring the change in position of the body relative to that frame with change in time. The branch of physics describing the motion of objects without regard to their cause is called kinematics, while the branch studying forces and their effect on motion are named dynamics.
If an object isn't changing relative to a given frame of reference, the thing is said to be at rest, motionless, immobile, stationary, or to possess a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there's no absolute frame of reference, Newton's concept of absolute motion can't be determined
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Two narrow slits spaced 100 microns apart are exposed to light of 600 nm. At what angle does the first minimum (dark space) occur in the interference pattern
Answer:
The angle is \(\theta = 0.1719^o\)
Explanation:
From the question we are told that
The distance of separation is \(d = 100 * 10^{-6} \ m\)
The wavelength of light is \(\lambda = 600 nm = 600 *10^{-9} \ m\)
Generally the condition for destructive interference is mathematically represented as
\(dsin(\theta ) =[m + \frac{1}{2} ]\lambda\)
Here m is the order of maxima, first minimum (dark space) m = 0
So
\(100 *10^{-6 } * sin(\theta ) =[0 + \frac{1}{2} ]600 *10^{-9}\)
=> \(\theta = sin^{-1} [0.003]\)
=> \(\theta = 0.1719^o\)
The king's chamber of the great pyramid is 10.43 meters long, 5.21 meters wide, and 5.82 meters high. What is the volume of the chamber in cubic feet? (meter=3.281ft)
Answer: 1037.65085143 cubed ft
Explanation:
Ok.
We apply the formula
l*w*h
10.43*5.21*5.82 = 316.260546 now * 3.281
1037.65085143 cubed ft
What is buoyancy? How is it related to the force of gravity?
Answer:
buoyancy is the ability to float on water or other liquids. this relates to the force of gravity because the stronger that force, the more likely it is to sink.
Explanation:
Which is true about scientific theories?
Group of answer choices
They are the result of a single experiment.
They are proposed by scientists who wish to investigate a new topic.
They are only based on the most recent evidence.
They are the results of many experiments over a long period of time.
Scientific theories are the results of many experiments over a long period of time.
Scientific theories are explanations that have been developed through extensive experimentation and observation over a period of time. They are supported by a large body of evidence from multiple sources and have been subjected to rigorous testing and scrutiny by the scientific community. Scientific theories are not based on a single experiment but rather on a vast accumulation of knowledge and data. They provide a framework for understanding the natural world and can help predict future observations and experiments. Scientific theories are also subject to change or revision if new evidence is discovered that contradicts or expands upon the existing theory. The development of scientific theories is a collaborative effort among scientists from different disciplines, and the peer-review process is used to ensure that scientific theories are reliable and accurate representations of reality. Scientific theories have been used to make significant advancements in fields such as medicine, engineering, and physics, and they continue to play a critical role in advancing our understanding of the world.
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module 2 question 13
Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force of 75.0 N, the second a force of 90.0 N, friction is 12.0 N, and the mass of the third child plus wagon is 22.0 kg.
(a) What is the system of interest if the acceleration of the child in the wagon is to be calculated? (Select all that apply.)
the children outside the wagon
the child in the wagon
the wagon
(b) Draw a free body diagram, including the weight and all other forces acting on the system. (Do this on paper. Your instructor may ask you to turn in this diagram.)
(c) Calculate the acceleration.
m/s2
(d) What would the acceleration be if friction is 15.0 N?
The acceleration of children will be 0.136m/s²
We are given that,
The first child exert force= F₁ = 75.0 N
The second child exerts force = F₂ = 90.0N
The friction force = Fₓ = 12.0 N
The mass of the third child = m = 22.0 kg
The first child & second child exert force 75 N and 90 N which are acting in opposite direction.
Therefore, the net force = F₂ - F₁ = 90 - 75 = 15 N
Friction force Fₓ would be act in the direction opposite to the direction of net force. So that the friction force will act in the direction in which the first child F₁ (75 N) is acting .
Total force acting in the direction of the second child= F₁+ Fₓ=75+12= 87 N
Net force acing on the third child F = 90 - 87 = 3 N
Therefore, the acceleration of the child can be calculated by the Newton's second law of motion i.e.
F = ma
a = F /m
a = 3N /22kg
a = 0.136 m/s²
Thus, the acceleration of the child will be 0.136 m/s²
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You are exploring a small moon of a distant planet. Measurements indicate that this moon is a sphere of uniform density rho = 5000 kg/m3. You dig a very deep hole into the moon that reaches within r0 = 1000 m of the center of the moon. With your spacesuit, you have a mass of m = 85 kg. Find the force of gravity on you when you stand at the bottom of the hole.
Answer:
The force of gravity will be "0.11874 N"
Explanation:
The given values are:
Density of planet,
Q = 5000 Kg/m³
Inside radius,
r₀ = 1000 m
Now,
The mass of inside sphere will be:
⇒ \(m_p=density\times volume\)
⇒ \(=5000\times \frac{4}{3}\pi r^3\)
On putting the values, we get
⇒ \(=5000\times \frac{4}{3}\times \pi\times (1000)^3\)
⇒ \(=85 \ kg\)
hence,
The force of gravity will be:
= \(\frac{Gm_{planet} m_{person}}{r^2}\)
= \(\frac{6.67\times 10^{-11}\times 5000\times 4\pi\times 85\times 1000}{3}\)
= \(\frac{6.67\times 10^{-11}\times 4\pi\times 425000000}{3}\)
= \(0.11874 \ N\)
In which of these situations is the most work being done? A ) Jeremy pushed a car up a steep B) Joe rolled a wagon down a small C) Jenny stood on one leg for 15 minutes D ) Johnny rolled a skateboard across his driveway.
Answer:
A)
Explanation:
Jeremy Pushed a car up a steep.
Answer:
a
Explanation:
I took the test s oooooooooooo
anybody knows what's is diffraction of waves
Answer: the spreading of waves around obstacles
Explanation:
One atomic mass unit is defined as 1.66 x 10^-27 kg. If a proton has a mass of one atomic mass unit and a density of approximately 5.8 x 10^27 kg/m3^ . What is the diameter of a proton if we assume it is a sphere?
Answer:
The diameter is \(d = 8.18*10^{-19} \ m\)
Explanation:
From the question we are told that
The value of one atomic mass unit is \(u = 1.66 *10^{-27} \ kg\)
The density of the proton is \(\rho = 5.8 *10^{27} \ kg/m^3\)
Generally the volume of the proton (sphere)is mathematically represented as
\(V = \frac{4}{3} * \pi * r^3\)
Generally this volume can also be evaluated as
\(V = \frac{u}{\rho}\)
=> \(V = \frac{1.66 *10^{-27}}{5.8*10^{27}}\)
=> \(V = 2.862 *10^{-55} \ m^3\)
So
\(2.862 *10^{-55} = \frac{4}{3} * 3.142 * r^3\)
=> \(r^3 = 6.832 *10^{-56}\)
=> \(r = 4.088 *10^{-19} \ m\)
Now the diameter is mathematically represented as
\(d = 2 * r\)
=> \(d = 2 * 4.088 *10^{-19}\)
=> \(d = 8.18*10^{-19} \ m\)
The figure above shows 4forces 3N, 10N, 3√3N, and 6N acting on a particle P. The resultant of the four forces is.
As you gave no pic I took them on one lined
F_1=3NF_2=10NF_3=3root 3 NF_4=6N\(\\ \sf\longmapsto F_{net}=F_1+F_2\dots\)
\(\\ \sf\longmapsto F_{net}=3+10+6+3\sqrt{3}\)
\(\\ \sf\longmapsto F_{net}=19+3(1.732)\)
\(\\ \sf\longmapsto F_{net}=19+5.196\)
\(\\ \sf\longmapsto F_{net}=24.196N\)
Tick the correct drills you can use to practise digging in volleybell a. double decker b. shuffle steps c. knock out drill 1. toss catch drill
The correct drills that can be used to practice digging in volleyball are b. shuffle steps and c. knock out drill.
b. Shuffle steps: Shuffle steps are an essential footwork drill for improving defensive movements, including digging.
In this drill, players shuffle laterally in a low defensive stance, simulating the movements required to dig a ball. It helps players develop quick and efficient footwork, enabling them to react and move quickly to reach the ball for a dig.
c. Knock out drill: The knock out drill focuses on improving a player's reaction time and defensive skills. In this drill, players form a line and take turns receiving rapid hits or "knocks" from a coach or teammate.
The objective is to successfully dig each hit and keep the ball in play.
This drill helps players develop their reflexes, positioning, and technique when digging in various directions and angles.
a. Double decker and 1. toss catch drill are not specific drills for practicing digging in volleyball. Double decker is a term used to describe a defensive formation, while the toss catch drill is more focused on developing ball control and setting skills rather than digging.
By incorporating shuffle steps and the knock out drill into practice sessions, players can enhance their digging abilities, improve their defensive movements, and develop the necessary skills to successfully retrieve hard-driven balls in a game situation.
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A 232g ball hangs on the end of a spring. When the spring is pulled down it oscillates with a period of .13s. When pull down too far to a point .56m below the equilibrium position, the ball flies off the spring when it reaches its equilibrium position, and flies into the air.
Find the spring constant
Find the height the ball reaches.
The spring constant is 542 N/m.
The height the ball reaches is 37.5 m.
Angular speed of the ball
The angular speed of the ball is calculated as follows;
ω = 2π/T
ω = (2π) / (0.13)
ω = 48.33 rad/s
Spring constantThe spring constant is calculated as follows;
ω = √(k/m)
ω² = k/m
ω²m = k
(48.33² x 0.232) = k
542 N/m
Linear speed of ballv = ωL
v = 48.33 x 0.56 m
v = 27.1 m/s
Height reached by the ballh = v²/2g
h = (27.1²) / (2 x 9.8)
h = 37.5 m
Thus, the spring constant is 542 N/m.
The height the ball reaches is 37.5 m.
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015
10.0 points
A car traveling in a straight line has a velocity
of 5.25 m/s at some instant. After 4.27 s, its
velocity is 9.38 m/s.
What is its average acceleration in this time
interval?
Answer in units of m/s.
Divide the change in speed by the given time:
a = (9.38 m/s - 5.25 m/s) / (4.27 s) ≈ 0.967 m/s²
Select all of the following that are involved in translation:
amino acids
tRNA
mRNA
ribonucleotides
deoxyribonucleotides
RNA Polymerase
Answer:
Amino Acids
tRNA
mRNA
ribonucleotides
Explanation:
Amino Acids
- During translation, an mRNA sequence is read using the genetic code, which is a set of rules that defines how an mRNA sequence is to be translated into the 20-letter code of amino acids, which are the building blocks of proteins.
tRNA
- At the beginning of translation, the ribosome and a tRNA attach to the mRNA. The tRNA is located in the ribosome's first docking site. This tRNA's anticodon is complementary to the mRNA's initiation codon, where translation starts. The tRNA carries the amino acid that corresponds to that codon. ransfer ribonucleic acid (tRNA) is a type of RNA molecule that helps decode a messenger RNA (mRNA) sequence into a protein. tRNAs function at specific sites in the ribosome during translation, which is a process that synthesizes a protein from an mRNA molecule.
mRNA
- Translation is the process by which a protein is synthesized from the information contained in a molecule of messenger RNA (mRNA). ... Then a transfer RNA (tRNA) molecule carrying the amino acid methionine binds to what is called the start codon of the mRNA sequence.
ribonucleotides
- During transcription, a ribonucleotide complementary to the DNA template strand is added to the growing RNA strand and a covalent phosphodiester bond is formed by dehydration synthesis between the new nucleotide and the last one added.
The scatter plot shows the number of minutes Guya practiced the flute each day in a given week.
How many minutes did Guya practice on Tuesday?
A) 1min
B) 2min
C) 20min
D) 30 min
If the scatter plot shows the number of minutes Guya practiced the flute each day in a given week, then Guya practiced 20 minutes on Tuesday, therefore the correct answer is option C.
What is a scatter plot?A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they may demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics.
As given in the problem If the scatter plot shows the number of minutes Guya practiced the flute each day in a given week,
The x coordinates is showing the days of practice and the y coordinate is showing the number of minutes he practiced the flute on a given day,
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How can i find Air velocity??????????????
Answer: By dividing airflow by duct cross section.
Explanation:
In short, air velocity in the ducts is calculated by dividing airflow by duct cross-section. Airflow is expressed as a simple number. Example: Air conditioner has a max. airflow of 600 CFM.
Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Calculate the acceleration of gravity on the surface of Kepler-62e.
Answer:
g' = 13.5 m/s²
Explanation:
The acceleration due to gravity on surface of earth is given by the formula:
g = GMe/Re² --------------- euation 1
where,
g = acceleration due to gravity on surface of earth
G = Universal Gravitational Constant
Me = Mass of Earth
Re = Radius of Earth
Now, the the acceleration due to gravity on the surface of Kepler-62e is:
g' = GM'/R'² --------------- euation 1
where,
g' = acceleration due to gravity on surface of Kepler-62e
G = Universal Gravitational Constant
M' = Mass of Kepler-62e = 3.57 Me
R' = Radius of Kepler-62e = 1.61 Re
Therefore,
g' = G(3.57 Me)/(1.61 Re)²
g' = 1.38 GMe/Re²
using equation 1:
g' = 1.38 g
where,
g = 9.8 m/s²
Therefore,
g' = 1.38(9.8 m/s²)
g' = 13.5 m/s²
What would the mechanical advantage of a ramp be if the length is 20 feet and the height is 5 feet?
100
8
1000
4
please use a multiple choice answer for branliest (how ever you spell it)
What is the potential energy of a 12 kg box on a 5 m high shelf?
Answer:6
Explanation:$’n
A 1.7 m tall person is standing 2.5 m in front of a camera. The camera uses a converging lens whose focal length is 0.05 m.
a) Find the image distance (between the lens and film) and determine whether the image is real or virtual.
b) Find the magnification and the height of the image on the film.
a)The image distance is 0.0075 m, and the image is real.
b) The magnification is -233.3, and the height of the image on the film is -3.99 m. A negative magnification indicates that the image is inverted
What is meant by image distance and Magnification?Independent of the original object's height and distance, magnification is a lens' inherent quality. If we were to move a toy car toward the lens, not only would the distance between the item and the lens diminish, but so would the distance between the image.
The height of the picture divided by the height of the object is known as the magnification produced by a lens. The ratio of the image distance to the object distance is used to define a lens's magnification.
Lens theory states that "(1)/(v) + (1)/(u) = (1)/(f)", where v is the image's distance from the lens, u is the object's distance from the lens, and f is the lens's focal length.
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Calculate Time
d
12. A vehicle drives a distance of 26000 m at a speed of 65m/s, calculate the time taken for
this journey.
13. A train travels at a speed of 16 m/s and travel a distance of 3200 m, calculate the time it
takes the train to complete this journey.
urs 14. Calculate the time it takes to travel a distance of 672 km at a speed of 96 km/h.
15. A beetle travels at a speed of 0.09 m/s, it travels a distance of 1.08 m before it is caught
in a jar. Calculate the time taken for the beetle to run.
16. Carlisle is a distance of 35 miles away from Lockerbie. If I travelled at a constant speed
5147
deudate the time takon for this journey
12. The time taken for the journey is 400 s
13. The time taken for the train is 200 s
14. The time taken is 7 h
15. The time taken for the beetle is 12 s
16. The time taken for the journey is 0.0068 h
How do i determine the time taken?The time taken in each case as given by the question can be obtain as follow:
12. The time taken for the journey
Distance traveled = 26000 mSpeed = 65 m/s Time taken =?Time taken = Distance / Speed
Time taken = 26000 / 65
Time taken = 400 s
13. The time taken for the train
Distance traveled = 3200 mSpeed = 16 m/s Time taken =?Time taken = Distance / Speed
Time taken = 3200 / 16
Time taken = 200 s
14. The time taken to travel
Distance traveled = 672 kmSpeed = 96 Km/h Time taken =?Time taken = Distance / Speed
Time taken = 672 / 96
Time taken = 7 h
15. The time taken for the beetle
Distance traveled = 1.08 mSpeed = 0.09 m/s Time taken =?Time taken = Distance / Speed
Time taken = 1.08 / 0.09
Time taken = 12 s
16. The time taken for the journey
Distance traveled = 35 milesSpeed = 5147 mile per hourTime taken =?Time taken = Distance / Speed
Time taken = 35 / 5147
Time taken = 0.0068 h
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when viewed through a formalist lens the point of
We can see that Shakespeare's structure when viewed through a formalist lens is to: C. Introduce a new motif that focuses on the inevitability of death.
Who is William Shakespeare?
William Shakespeare was known as an English actor, poet and also a playwright. Many regard Shakespeare as the greatest writer in the English language. He is often seen as the world's greatest dramatist.
William Shakespeare was known to have written several plays like:
Romeo and JulietMacbethThe Tragedy of Julius Caesar, etc.The reader aims to comprehend how words interact with one another and how different parts of the text relate to one another.
Therefore, William Shakespeare employ this technique in his study and is likely to be interested in how the various components of the text interact.
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A girl is sledding down a slope that is inclined at 30.0° with respect to the horizontal. The wind is aiding the motion by providing asteady force of 159. N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 58.8 kg, and thecoefficient of kinetic friction between the snow and the runners of the sled is 0.113. How much time is required for the sled to traveldown a 223-m slope, starting from rest?
Let's draw the free body diagram:
Using newton's second law:
\(\begin{gathered} \Sigma Fy=0 \\ so: \\ Wcos(30)-N=0 \\ so: \\ mgcos(30)=N \end{gathered}\)\(\begin{gathered} \Sigma Fx=ma \\ F+mgsin(30)-Ff=ma \\ a=\frac{F+mgsin(30)-Ff}{m} \end{gathered}\)We can solve for a using the values provided by the problem:
\(\begin{gathered} a=\frac{159+58.8(9.8)sin(30)-\mu N}{m} \\ a=\frac{159+58.8(9.8)s\imaginaryI n(30)-(0.113)(58.8)(9.8)cos(30)}{58.8} \\ so: \\ a\approx6.645m/s^2 \end{gathered}\)Now, we can use the following kinematic equation:
\(\begin{gathered} d=\frac{1}{2}at^2 \\ t^2=\frac{2d}{a} \\ t=\sqrt{\frac{2d}{a}} \\ t=\sqrt{\frac{2(223)}{6.645}} \\ t\approx8.19s \end{gathered}\)Answer:
8.19 seconds
A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?
The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².
To calculate the average acceleration of the motorcycle, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.
Converting the final velocity:
Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s
Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:
Average acceleration = (21.67 m/s - 0 m/s) / time
To find the time taken to reach this velocity, we need to use the formula for average speed:
Average speed = total distance/time
Rearranging the formula:
time = total distance / average speed
Plugging in the values:
time = 50 m / 21.67 m/s ≈ 2.31 seconds
Now we can calculate the average acceleration:
Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²
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A ball rolls off a table and falls 0.75m to the floor, landing with a speed of 4 m/s. (A) What is the acceleration of the ball just before it strikes the ground? (B) What was the initial speed of the ball? (C) What initial speed must the ball have if it is to land with a speed of 5 m/s?
The acceleration of the ball is 21.33m/s²,
We are given that,
The ball fall's from height = d = 0.75m
The final speed of the ball = Vf = 4m/s
So that to know the acceleration of the ball we can calculate by the equation of motion in term of velocity and acceleration i.e. given as,
V = u + at
Where, V is the final velocity , u is the initial velocity , t is the time and a is the acceleration of the object.
t = d/v
t = (0.75m)/(4m/s)
t = 0.1875s
Thus, the value of t, V, and initial velocity is zero putting in equation of motion to get acceleration,
a = (4m/s)/(0.1875s)
a = 21.33m/s²
The acceleration of the ball would be 21.33m/s²
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The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged
that your client, Mr. Lawton, shot the victim, Mr. Cray. The detective who investigated the scene of the
crime, Mr. Dibny, found a second bullet, from a shot that missed Mr. Cray, that had embedded itself into a
chair. You arise to cross-examine the detective.
You: In what type of chair did you find the bullet?
Dinby: A wooden chair.
You: How massive was this chair?
Dinby: It had a mass of 20 kg.
You: How did the chair respond to being struck with a bullet?
Dinby: It slid across the floor.
You: How far?
Dinby: Three centimeters. The slide marks on the dusty floor are quite distinct.
You: What kind of floor was it?
Dinby: A wood floor.
You: What was the mass of the bullet you retrieved from the chair?
Dinby: Its mass was 10 g.
You: Have you tested the gun you found in Mr. Lawton's possession?
Dinby: I have.
You: What is the muzzle velocity of bullets fired from that gun?
Dinby: The muzzle velocity is 450 m/s.
With only slight hesitation, you turn confidently to the jury and proclaim, "My client's gun did not fire those
shots!"
(a) How are you going to convince the jury and judge?
(b) Choose one part of your solution and perform a sense-making analysis. Clearly state which sensemaking analysis you’ve chosen and why.
Answer:
It was not fired from the client's gun because the chair slid only 3 centimeters . If it had been fired from the client's gun the chair would slid 25.82 centimeters.
Explanation:
According to the law of conservation of momentum the momentum of the system before collision must be equal to the momentum of the system after the collision.
M1u1= m2u2
Let M1 = mass of the chair = 20kg
m2= mass of the bullet= 10g= 0.001kg
u1= velocity of the chair before collision = zero m/s
u2 = velocity of the bullet before collision = zero m/s
v1= velocity of the chair after collision = ? m/s
v2 = velocity of the bullet after collision = 450 m/s
After collision their velocities change from u1 to v1 and u2 to v2 so
M1v1= m2v2
v1= m2v2/M1
v1= 0.01 *450/ 20= 0.225 m/s
Now according to the law of conservation of energy the energy of the system before collision must be equal to the energy of the system after the collision.
The energy of the chair after the bullet is hit is
KE of the chair + KE of the bullet= 1/2 (M)(v1)²+ 1/2 m(v2)²=
1/2 ( 20) (0.225 )² + 1/2 (0.01) (450)²
= 0.50625 + 1012.5= 1013.00625 Joules
Frictional force = Coefficient of kinetic force of wood on wood ( M+m) g
= 0.2* ( 20.01) 9.8= 39.2196 N
Work done by friction = frictional force * distance
If law of conservation of energy is applied the KE must be equal to the work done
KE = W
W= f*d
KE= F*d
d = KE/f= 1013.00625/ 39.2196= 25.82 cm
The chair did not move 25.82 cm .
It only moved 3 centimeter.
Hence the bullet fired was not from the client's gun.