A rocket is attached to a person in a sled with a combined mass of 79 kg. The sled is launched with 358 N of thrust up a frictionless icy hill sloped at 17.4° from the horizontal. What is the magnitude of acceleration of the sled while it travels up the hill?

Answer:

0.75 grams

Explanation:

Today we have 6 grams

In 30 years, 3 grams remain

In 60 years 1.5 grams remain

in 90 years 0.75 grams remain

mathematically It would look like this

m = 6(0.5⁽ⁿ/³⁰⁾) where n is number of years

The power to stop the car with kinetic energy of a car is  \(8*10^{6} J\) as it travels along a horizontal road is  \(8*10^{5} watt\), option B

Kinetic energy can be seen as one that is been recorded when an object is able to move from a place , in a broad term we can say this is the energy that can be attributed to that of someone leaving a place and go to another place hence we can see it as the one in the motion.

The definition of energy as the "power to accomplish work" refers to the capacity to apply a force that moves an object. Even if the word is vague, it is clear what energy actually means: it is the force that causes objects to move. The two types  can be attributed to the one we know which are kinetic and potential energy.

\(Power \frac{Energy}{time}\)

\(Energy = 8*10^{6} J\)

\(time = 10 s\)

\(Power = \frac{8*10^{6} J}{10}\)

\(power = 8*10^{5} watt\)

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proper question;

The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? (A) zero joules (B) 8  105 J (C) 8  107 J (D)8  104 J (E) 8  106 J​

The height that will illustrate the distance will be d = 6.36m

Based on the information given, the length of the vine will be:

L = ✓(16² + 27.7)²

L = 32m

The velocity of Jane when she reaches position B will be:

V = ✓2gh

V = ✓(2 × 9.8 × 4.3)

V = 9.18m/s

We will apply the conversation of momentum. This will be:

50 × 9.18 = (50 + 80)V1

V1 = 3.53m/s

Therefore, the height that will illustrate the distance will be:

31.36² + d² = 32²

d² = 32² - 31.36²

d = 6.36m

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The force actually being used to push the mower along the ground is 191 N.

When the physics student exerts a force of 250 N along the handle of the push mower, it's important to consider the components of this force that contribute to the actual force used to push the mower along the ground.

To determine the force used to push the mower along the ground, we need to find the horizontal component of the applied force. The angle of 40° indicates that the applied force can be broken down into two components: the horizontal component and the vertical component. The vertical component of the force is perpendicular to the direction of motion and does not contribute to pushing the mower forward.

To find the horizontal component, we can use trigonometry. The horizontal component is given by the formula:

Horizontal component = Applied force * cos(angle)

Plugging in the values, we get:

Horizontal component = 250 N * cos(40°)

Calculating this value, we find that the horizontal component of the applied force is approximately 191 N.

Therefore, the force actually being used to push the mower along the ground is 191 N. This is the component of the applied force that contributes to the forward motion of the mower, while the remaining vertical component is directed perpendicular to the ground and does not assist in pushing the mower forward.

By exerting a force of 250 N along the handle at a 40° angle, the student effectively applies 191 N of force to push the mower along the ground, ensuring efficient use of their effort while considering the environmental impact.

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To determine the impulse we use the fact that the impulse is equal to the change in momentum:

Where:

The momentum is the product of the mass and the velocity, therefore, we have:

Since the initial velocity is zero, we have:

Now, we substitute the values:

Solving the operation:

Therefore, the momentum is 1607424 kgm/s

Answer:

Explanation:

Focal length (f) can be defined as the distance from the focal point to the centre of the surface of the mirror.

While radius of curvature (r) is the radius of the sphere of which the mirror forms a part.

Hence the relationship between the two is that the focal length is half of the length of the radius of curvature.

Mathematically,

F = r/2

Explanation:

Identify the THREE type of relationships illustrated in the cartoon above

Answer:

D

Explanation:

The elevator is either moving upwards with an increasing speed, or moving downwards with a a decreasing speed.

The statement above is true because the direction at which the elevator accelerates, or decelerates(which is negative acceleration anyway), is of paramount importance. If the acceleration is towards the upside, the apparent weight does becomes greater than the true weight. While on the other hand, if the acceleration points towards the downside, then the apparent weight does becomes less than the true weight.

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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Answer:

The motion of a body about a fixed point or fixed axis.

Explanation:

Brainly

Answer:Force is to the right

Explanation: because the right side has 75N compared to the 25N on the left.

Answer:

a) The laser device

b) The tape

Explanation:

First, there is a need to understand what accuracy and precision mean.

Accuracy is the closeness of a measurement to its true (pre-determined) value.

Precision is the closeness of repeated measurements to each other.

Since 1 feet = 12 inches, then, 5 feet and 5.2 inches would be equivalent to 65.2 inches. This value represents the true value of my height.

The tape measured the height as 65 3/8, which is equivalent to 65.375 inches.

The laser device measured the height as 65.31.

Error = true value - measured value

Absolute error from the tape = 65.2 - 65.375

                                       = -0.175 inches

Absolute error from laser device = 65.2 - 65.31

                                 = -0.11

a) The magnitude of error from the tape is more than that of the laser device. Hence, the laser device is said to be more accurate.

b) Even though there were just single readings from both instruments, the tape can be read to the nearest 1/8 of an inch and as such, can give more precisive measurements than the laser device.

The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.

To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.

The force between two charged particles can be calculated using Coulomb's law:

F = k * |q₁ * q₂| / r²

Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.

First, let's calculate the force exerted on q₂ by q₁:

F₁₂ = k * |q₁ * q₂| / r₁₂²

F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²

F₁₂ ≈ 252000 N

The force is positive because q₁ and q₂ have opposite charges.

Next, let's calculate the force exerted on q₂ by q₃:

F₂₃ = k * |q₂ * q₃| / r₂₃²

F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²

F₂₃ ≈ -63000 N

The force is negative because q₂ and q₃ have the same charge.

Finally, we can find the net force on q₂ by summing the individual forces:

Net force = F₁₂ + F₂₃

Net force = 252000 N + (-63000 N)

Net force ≈ 189000 N

The net force on particle q₂ is approximately 189000 N.

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The magnitude of the magnetic field at point P is equal to 0.24μT.

A magnetic field can be described as a vector field that has a magnetic influence on electric currents, moving electric charges, and magnetic materials.

The equation for the Magnetic field  can be mathematically represented as:

\(\diaplystyle B = \frac{\mu }{ 4\pi} \times \frac{(qv )}{r^2}\)

A point charge Q moves on the x-axis in the +ve direction with a speed of 370 m/s.

A point P on the y-axis at y = +80 mm

The magnetic field at point P, B = -0.3 μT  = -0.3 ×10⁻⁶ T

The position of charge on the x-axis, x = +40 mm = 40 ×10⁻³ m

Mathematically, the magnitude of the charge is calculated as:

q =  B₀ 4π.y²/μ₀v

q = -0.3 ×10⁻⁶ ×4 ×3.14×(80 ×10⁻³)²/ 4π × 10⁻⁷× 370)

q = - 52 ×10⁻⁶ C

The distance from the position of the charge to point P is:

\(r =\sqrt{x^2 +y^2}\\ r = 0.08944 m\)

The magnitude of  the magnetic field at point P will be:

\(\diaplystyle B = \frac{\mu }{ 4\pi} \times \frac{(qv )}{r^2}\)

\(\diaplystyle B = \frac{4\pi \times 10^{-7} }{ 4\pi} \times \frac{(52\times 10^{-6} )\times 370}{(0.08944)^2}\)

B = 0.24 ×10⁻⁶ T

B = 0.24 μT

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The absolute pressure at an ocean depth of 1.0 x 10^3 m is 1.002 x 10^8 Pa.

Hydrostatic pressure is the pressure that a fluid exerts on a surface due to the weight of the fluid above it. It is the result of the force of gravity acting on a column of fluid, and it is directly proportional to the height of the column of fluid and the density of the fluid.

The absolute pressure at an ocean depth of 1.0 x 10^3 m can be calculated using the hydrostatic pressure equation:

P = ρgh + Po

where:

P is the absolute pressure at the given depth

ρ is the density of the water

g is the acceleration due to gravity (assumed to be 9.81 m/s²)

h is the depth of the ocean

Po is the atmospheric pressure at the surface (assumed to be 1.01 x 10^5 Pa)

Substituting the given values, we get:

P = (1.025 x 10^3 kg/m³) x (9.81 m/s²) x (1.0 x 10^3 m) + 1.01 x 10^5 Pa

P = 1.025 x 9.81 x 10^6 Pa + 1.01 x 10^5 Pa

P = 1.002 x 10^8 Pa.

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Answer:

The value of g is  \(g =76.2 m/s^2\)

Explanation:

From the question we are told that

     The mass of the weight is \(m = 1.30 kg\)

      The spring  constant  \(k = 1.73 g/m = 1.73 *10^{-3} \ kg/m\)

       The second harmonic frequency is \(f = 100 \ Hz\)

       The number of oscillation is \(N = 200\)

        The time taken is  \(t = 315 \ s\)

Generally the frequency is  mathematically represented as

           \(f = \frac{v}{\lambda}\)

At second harmonic frequency the length of the string vibrating is equal to  the wavelength of the wave generated

         \(l = \lambda\)

Noe from the question the vibrating string is just half of the length of the main string so

Let assume the length of the main string is  \(L\)

So      \(l = \frac{L}{2}\)

The velocity of the vibrating string is mathematically represented as

             \(v = \sqrt{\frac{T}{\mu} }\)

Where T is the tension on the string which can be mathematically represented as

             \(T = mg\)

So  

           \(v = \sqrt{\frac{mg}{k} }\)

Then

          \(f = \frac{v}{\frac{L}{2} }\)

=>       \(v = \frac{fL }{2}\)

=>      \(\sqrt{\frac{mg}{k} } = \frac{fL}{2}\)

=>        \(g = \frac{f^2 L^2 \mu}{4m}\)

substituting values

             \(g = \frac{(100) * (1.73 *10^{-3} )}{(4 * 1.30)} L^2\)

              \(g = 3.326 m^{-1} s^{-2} L^2\)

Generally the period of oscillation is mathematically represented as

       \(T_p = 2 \pi \sqrt{\frac{L}{g} }\)

=>   \(L = \frac{T^2 g}{4 \pi ^2}\)

   The period can be mathematically evaluated as

                \(T_p = \frac{t}{N}\)

 substituting values

             \(T_p = \frac{315}{200}\)

             \(T_p = 1.575 \ s\)

Therefore

          \(L = \frac{1.575^2 * g }{4 \pi ^2}\)

           \(L = 0.0628 ^2 g\)

so

      \(g = 3.326 m^{-1} s^{-2} L^2\)

substituting for L

        \(g = 3.326 ((0.0628) g)^2\)

=>    \(g = \frac{1}{(3.326)* (0.0628)^2}\)

       \(g =76.2 m/s^2\)

The height of the cliff from which a rock of 5 kg falls is 12.2 m.

Height is the vertical distance between two points.

To calculate the heigth of the cliff, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the height of the clifff is 12.2 m.

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a. The velocity must remain constant to keep the ratio of frequency and wavelength in check. The wave speed is determined by the properties of the medium through which the wave travels, and is independent of the frequency and wavelength of the wave.

c. 0.35 m. The wavelength can be calculated using the formula: wavelength = wave speed / frequency. Plugging in the given values, we get wavelength = 4.5 m/s / 25 Hz = 0.18 m/Hz = 0.35 m (rounded to two decimal places).

Answer:

vt3bryhtevy4g24vu5hy4

the order of average normal stress developed on cross section through B, C and D c) B>C>D.

When examined at constant levels of the applied shear stress s, the initial stress distribution differences N1 (cv) show a decreasing trend as the solid fraction cv increases.In other words, the shear stress increases more quickly than the usual stress differential does with filler volume fraction.

How is the typical soil stress determined?

EF is the area, and is the stress, hence F1 = EF.EF = EF = θ θ θ θ θ θ = θ θ θ θregular stress on the plane's EF.We can select the value of from this equation in a way that it equals zero.The primary plane is the one that forms this angle with block, which only experiences normal stress.

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The Ceres is (a).The largest asteroid identified to date is correct option.

With a diameter of around 590 miles (940 km), Ceres is the biggest asteroid between Mars and Jupiter. It is regarded as a minor planet, like Pluto, and was found in 1801 by Giuseppe Piazzi. Ceres is made of rock and ice, and due to its low density, it is likely that it contains a substantial amount of water ice inside.

The NASA Dawn spacecraft visited Ceres in 2015 and orbited the dwarf planet for more than three years, gathering useful information and taking stunning pictures of it.

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Answer:

D:#2 African Plate

Explanation:

The African Plate is flanked by the Red sea rift and the minor African plate.

The Red sea rift is a small part of a greater line of rifts known as the Great African Rift Valley. The rift valley is making several small lakes all through Africa and it will eventually split up the African continent.

The Red sea lift is the divergent boundary between the African plate and the Arabian plate. It means that the two plates are moving apart or spreading apart.

Answer:

what :D

Explanation:

Answer:

The initial momentum of the ball is 8 kg-m/s.

Explanation:

Given that,

Mass of the ball is 4 kg

Initial speed of the ball is 2 m/s

Force applied to the ball is 5 N for 3 seconds

It is required to find the initial momentum of the ball. Initial momentum means that the product of mass and initial velocity of the ball. It is given as :

\(p_i=mu\\\\p_i=4\ kg\times 2\ m/s\\\\p_i=8\ kg-m/s\)

So, the initial momentum of the ball is 8 kg-m/s.

Drawing (d) best represents the system after the stopcocks are opened and the system is allowed to come to equilibrium, as it shows equal pressure in all three bulbs.

Since the two bulbs contain different gases, the pressures in each bulb will be different. When the stopcocks are opened, the gases will flow into the empty bulb until the pressures are equalized. The final state will have equal pressure in all three bulbs.

What is an equilibrium?

An equilibrium is a state of balance or stability achieved in a chemical reaction when the forward reaction rate is equal to the reverse reaction rate. In other words, it is the point at which the concentrations of reactants and products no longer change with time, because the rates of the forward and reverse reactions are equal.

At equilibrium, the amounts of reactants and products are governed by the equilibrium constant (K), which is a measure of the relative concentrations of the reactants and products at equilibrium.

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When the liquid cools down, it loses heat energy.

As the liquid cools, it loses heat energy. As a result, its particles slow down in movement and come closer to one another. Attractive forces begin to hold particles and the crystals of a solid form.

If water is cooled, it can change into ice. If ice is warmed, it can change into a liquid state. Heating a substance makes the molecules move very fast whereas cooling a substance makes the molecules move very slowly.

Heating a liquid increases the speed of the molecules present in it. An increase in the molecule's speed competes with the attraction between molecules and results in the molecules moving apart whereas Cooling a liquid decreases the movement of the molecules.

So we can conclude that the liquid cools down when it loses heat energy.

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Acceleration of the skydiver during the free fall is 4.13 m/s².

1) Mass of the skydiver, m = 83 kg

Weight, W = mg = 83 x 9.8

W = 813.4 N

Free fall acceleration is the acceleration that a body travelling in free fall experiences due to only the gravitational pull of the earth. This is the acceleration brought on by gravity.

Since there is no air resistance, the acceleration of the skydiver during the free fall is the acceleration due to gravity, g.

Freebody diagram is given in Fig.1.

2) Mass of the skydiver, m = 78 kg

Air resistance acting on him, F' = 470 N

mg - 470 = ma

813.4 - 470 = ma

a = 343.4/83

a = 4.13 m/s²

Freebody diagram is given in fig.2.

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Answer:

(a) 4.83 seconds

(b) 167.3m

(c) 40m

Explanation:

This is a two-dimensional motion. Therefore, the components of the initial velocity - \(u_X\) and \(u_Y\) - in the x and y directions are given as follows:

\(u_X\) = u cos θ                 --------------(*)

\(u_Y\) = u sin θ                -------------(**)

Where

θ = angle of projection

(a) To calculate the time taken for the apple to strike the ground.

For simplicity, let's first calculate the maximum height H reached by the apple.

Using one of the equations of motion as follows, we can find H:

v² = u² + 2as               ---------------(i)

Where;

v = velocity at maximum height = 0 [at maximum height, velocity is 0]

u = initial vertical velocity of the apple = \(u_Y\)

=> u = \(u_Y\) = u sin θ

=> \(u_Y\) = 40 sin 30°

=> \(u_Y\) = 40 x 0.5

=> \(u_Y\) = 20 m/s

a = acceleration due to gravity = -g [apple moves upwards against gravity]

a = -10m/s²

s = H = maximum height reached from the top of the building

Substitute these values into equation (i) above to have;

0² = \(u_Y\)² + 2aH

0² = (20)² + 2(-10)H

0 = 400 - 20H

20H = 400

H = 20m

The total time taken to strike the ground is the sum of the time taken to reach maximum height and the time taken to strike the ground from maximum height.

=>Calculate time t₁ to reach maximum height.

Using one of the equations of motion, we can calculate t₁ as follows;

v = \(u_Y\)  + at                ---------------(ii)

Where;

v = velocity at maximum height = 0

u = initial vertical velocity of the apple = \(u_Y\)

a = -g = -10m/s²           [acceleration due to gravity is negative since the apple is thrown upwards to reach maximum height]

t = t₁ = time taken to reach maximum height.

Equation (ii) then becomes;

0 = 20  + (-10)t₁

10t₁ = 20

t₁ = 2 seconds

=>Calculate time t₂ to strike the ground from maximum height.

Now, using one of the equations of motion, we can calculate the time taken as follows;

Δy = \(u_Y\) t + \(\frac{1}{2}\)at                ---------------(iii)

Where;

Δy = displacement from maximum height to the ground = maximum height from top of building + height of building = 20 + 20 = 40m

a = g = 10m/s²            [acceleration due to gravity is positive since the apple is now coming downwards from maximum height]

t = t₂    [time taken to strike the ground from maximum height]

\(u_Y\) = initial vertical velocity from maximum height = 0

\(u_Y\) = 0

Equation (iii) then becomes

40 = 0t + \(\frac{1}{2}\)(10)t₂²

40 = 5t₂²            [divide through by 5]

8 = t₂²

t₂ = ±\(\sqrt{8}\)

t₂ = ±\(2\sqrt{2}\)

t₂ = +2\(\sqrt{2}\) or -2\(\sqrt{2}\)

since time cannot be negative,

t₂ = 2\(\sqrt{2}\) = 2.83 seconds

Therefore, the time taken for the apple to strike the ground is;

t₁ + t₂ = 2 +  2.83 = 4.83 seconds

(b) The distance from the foot of the building where the apple will strike the ground

Since this is the horizontal distance, we use the horizontal version of equation (iii) as follows;

Δx = \(u_X\) t + \(\frac{1}{2}\)at       -----------(v)

Where

Δx = distance from the foot of the building to where the apple strikes the ground.

\(u_X\) = initial horizontal velocity of the apple as expressed in equation (*)

\(u_X\) = 40 cos 30

\(u_X\) = 34.64 m/s

t = time taken for the motion of the apple = 4.83 seconds [calculated above]

a = acceleration due to gravity in the horizontal direction = 0. [For a projectile, there is no acceleration in the horizontal direction since velocity is constant]

Substitute these values into equation (v) as follows;

Δx = \(u_X\) t + \(\frac{1}{2}\)(0)t

Δx = 34.64 x 4.83

Δx = 167.3 m

Therefore, the distance from the foot of the building is 167.3m

(c) The maximum height reached by the apple from the ground

This is the sum of the height reached from the top of the building (20m which has been calculated in (a) above) and the height of the building.

= 20m + 20m = 40m

Answer:

To solve the problem we must know the concept of momentum.

What is Momentum?

Momentum is defined as the product of the mass of an object and the velocity of an object. It is a vector quantity.

$$\rm{Momentum = velocity \times Mass$$

The mass of the object is 50 kg.

Given to us

velocity of the object = 3.60 m/s

momentum of the object = 180 kg m/s

Mass of the object

We know that momentum is the product of the mass of the object and the velocity of the object,

$$\rm{Momentum = velocity \times Mass$$

Substitute the values,

180 = 3.60 \times \rm Mass180=3.60×Mass

\rm Mass = \dfrac{180\ kg\ m/s}{3.6\ m/s}Mass=

3.6 m/s

180 kg m/s

\rm Mass = 50\ kgMass=50 kg

Hence, the mass of the object is 50 kg.