# First Year Physics Motion and Force A bomber dropped a bomb at a height of 490 \mathrm{~m} when its velocity along the horizontal was 300 \mathrm{kmh}^{-1} .(a) At what distance from the point vertically below the bomber at the insta

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##### A bomber dropped a bomb at a height of 490 \mathrm{~m} when its velocity along the horizontal was 300 \mathrm{kmh}^{-1} .(a) At what distance from the point vertically below the bomber at the instant bomb was dropped did it strike the ground?

A boy places a fire cracker of negligible mass in an empty can of 40 \mathrm{~g} mass. He plugs the end with a wooden block of mass 200 \mathrm{~g} . After igniting the firecracker he throws the can straight up. It explodes at the top of its path. If the block shoots out with a speed of 3 \mathrm{~ms}^{-1} how fast will the can be going?

Explain the circumstances in which the velocity " v " and acceleration "a" of a car are:(iv) " v " " is zero but "a" is not

Explain the circumstances in which the velocity " v " and acceleration "a" of a car are:(v) "a" is zero but " v " is not zero

A hose pipe ejects water at a speed of 0.3 \mathrm{~ms}^{-1} through a hole of area 50 \mathrm{~cm}^{2} . If the water strikes a wall normally calculate the force on the wall assuming the velocity of the water normal to the wall is zero after striking.

Each of the following questions is followed by four answers one of which is correct answer. Identified that answer.(i) What is meant by a ballistic trajectory?(a) The paths followed by an un-powered and unguided projectile is called ballistic trajectory.(b) The path followed by the powered and unguided projectile is called ballistic trajectory.(c) The path followed by un-powered but guided projectile.(d) The path followed by powered and guided projectile.

A 1500 kg car has its velocity reduced from 20 \mathrm{~ms}^{-1} to 15 \mathrm{~ms}^{-1} in 3 . S . How large was the average retarding force.

Explain the circumstances in which the velocity " v " and acceleration "a" of a car are:(iii) Perpendicular to one another

Example 3.7: A ball is thrown with a speed of so 30 \mathrm{~ms}^{-1} in a direction 30^{\circ} above the horizon. Determine the height to which it rises the time of flight and the horizontal range.

A truck weighing 2500 \mathrm{~kg} and moving with a velocity of 21 \mathrm{~ms}^{-1} collides with a stationary car weighing 1000 \mathrm{~kg} . The truck and the car move together after the impact. Calculate their common velocity.

Using the following data draw a velocity-time graph for a short journey on a straight road of a motorbike.\begin{tabular}{|l|c|c|c|c|c|c|c|}\hline Velocity \left(\mathrm{ms}^{-1}\right) & 0 & 10 & 20 & 20 & 20 & 20 & 0 \\\hline Time (s) & 0 & 30 & 60 & 90 & 120 & 150 & 180 \\\hline\end{tabular}Use the graph to calculate(b) The final acceleration

Find the change in momentum for an object subjected to a given force for a given time and state law of motion in terms of momentum.

Prove that for angles of projection which exceed or fall short of 45^{\circ} by equal amounts the ranges are equal.

A helicopter is ascending vertically at the rate of 19.6 \mathrm{~ms}^{-1} . When it is at a height of 156.8 \mathrm{~m} above the ground a stone is dropped. How long does the stone take to reach the ground?

Example 3.5: A 100 \mathrm{~g} golf ball is moving to the right with a velocity of 20 \mathrm{~ms}^{-1} . It makes a head on collision with an 8 \mathrm{~kg} steel ball initially at rest. Compute velocities of the balls after collision.

Example 3.8: In example 3.7 calculate the maximum range and the height reached by the ball if the angles of projection are (i) 45^{\circ} (ii) 60^{\circ} .

Two blocks of masses 2.0 \mathrm{~kg} and 0.5 \mathrm{~kg} are attached at the two ends of a compressed spring. The elastic potential energy stored in the spring in 10 \mathrm{~J} . Find the velocities of the blocks if the spring delivers its energy to the blocks when released.

Each of the following questions is followed by four answers one of which is correct answer. Identified that answer.(ii) What happens when two-body system undergoes elastic collision?(a) The momentum of the system changes.(b) The momentum of the system does not change.(c) The bodies come to rest after collision.(d) The energy conservation law is violated.

A football is thrown upward with an angle of 30^{\circ} with respect to the horizontal. To throw a 40 mass what must be the initial speed of the ball?

An amoeba of mass 1.0 \times 10^{-12} \mathrm{~kg} propels itself through water by blowing a jet of water through a tiny orifice. The amoeba ejects water with a speed of 1.0 \times 10^{-4} \mathrm{~ms}^{-1} and at a rate of 1.0 \times 10^{-13} \mathrm{kgs}^{-1} . Assume that the water is being continuously replenished so that the mass of the amoeba remains the same.(a) If there were no force on amoeba other than the reaction force caused by the emerging jet what would be the acceleration of the amoeba?(b) If amoeba moves with constant velocity through water what is force of surrounding water (exclusively of jet) on the amoeba?

Two masses m_{1} and m_{2} are initially at rest with a spring compressed between them. What is the magnitude of ratio of their velocities after the spring has been released?

A bomber dropped a bomb at a height of 490 \mathrm{~m} when its velocity along the horizontal was 300 \mathrm{kmh}^{-1} .(b) How long was it in air?

A proton moving with speed of 1.0 \times 10^{7} \mathrm{~ms}^{-1} passes through a 0.02 \mathrm{~cm} thick sheet of paper and emerges with a speed of 2.0 \times 10^{6} \mathrm{~ms}^{-1} . Assuming uniform deceleration find retardation and time taken to pass through the paper.

Explain the circumstances in which the velocity "v" and acceleration "a" of a car are:(ii) Anti-parallel

An electron \left(\mathrm{m}=9.1 \times 10^{-31} \mathrm{~kg}\right) traveling at 2.0 \times 10^{7} \mathrm{~ms}^{-1} undergoes a head on collision with a hydrogen atom \left(\mathrm{m}=1.67 \times 10^{-27} \mathrm{~kg}\right) which is initially at rest. Assuming the collision to be perfectly elastic and a motion to be along a straight line find the velocity of hydrogen atom?

Using the following data draw a velocity-time graph for a short journey on a straight road of a motorbike.\begin{tabular}{|l|c|c|c|c|c|c|c|}\hline Velocity \left(\mathrm{ms}^{-1}\right) & 0 & 10 & 20 & 20 & 20 & 20 & 0 \\\hline Time (\mathrm{s}) & 0 & 30 & 60 & 90 & 120 & 150 & 180 \\\hline\end{tabular}Use the graph to calculate(a) The initial acceleration

Find the angle of projection of a projectile for which its maximum height and horizontal range are equal.

State the law of conservation of linear momentum pointing out the importance of isolated system. Explain why under certain conditions the law is useful even though the system is not completely isolated?

A SLBM (submarine launched ballistic missile) is fired from a distance of 3000 \mathrm{~km} . If the Earth were flat and the angle of launch is 45^{\circ} with horizontal find the time taken by SLBM to hit the target and the velocity with which the missile is fired.