Vertical motion: energy loss on impact

A question is this type if and only if a particle hits the ground, loses a specified amount of kinetic energy, and you must find subsequent motion (rebound height or time).

4 questions · Moderate -0.6

3.02h Motion under gravity: vector form
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CAIE M1 2014 June Q4
7 marks Moderate -0.3
4 A small ball of mass 0.4 kg is released from rest at a point 5 m above horizontal ground. At the instant the ball hits the ground it loses 12.8 J of kinetic energy and starts to move upwards.
  1. Show that the greatest height above the ground that the ball reaches after hitting the ground is 1.8 m .
  2. Find the time taken for the ball's motion from its release until reaching this greatest height.
Edexcel M1 2014 June Q3
13 marks Moderate -0.8
  1. A ball of mass 0.3 kg is released from rest at a point which is 2 m above horizontal ground. The ball moves freely under gravity. After striking the ground, the ball rebounds vertically and rises to a maximum height of 1.5 m above the ground, before falling to the ground again. The ball is modelled as a particle.
    1. Find the speed of the ball at the instant before it strikes the ground for the first time.
    2. Find the speed of the ball at the instant after it rebounds from the ground for the first time.
    3. Find the magnitude of the impulse on the ball in the first impact with the ground.
    4. Sketch, in the space provided, a velocity-time graph for the motion of the ball from the instant when it is released until the instant when it strikes the ground for the second time.
    5. Find the time between the instant when the ball is released and the instant when it strikes the ground for the second time.
Edexcel M1 2018 Specimen Q3
10 marks Moderate -0.3
3. A block \(A\) of mass 9 kg is released from rest from a point \(P\) which is a height \(h\) metres above horizontal soft ground. The block falls and strikes another block \(B\) of mass 1.5 kg which is on the ground vertically below \(P\). The speed of \(A\) immediately before it strikes \(B\) is \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The blocks are modelled as particles.
  1. Find the value of \(h\). Immediately after the impact the blocks move downwards together with the same speed and both come to rest after sinking a vertical distance of 12 cm into the ground. Assuming that the resistance offered by the ground has constant magnitude \(R\) newtons,
  2. find the value of \(R\). \includegraphics[max width=\textwidth, alt={}, center]{6ab8838f-d6f8-4761-8def-1022d97d4e82-07_2252_51_315_36}
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Edexcel M1 Q3
9 marks Moderate -0.8
A stone is dropped from rest at a height of 7 m above horizontal ground. It falls vertically, hits the ground and rebounds vertically upwards with half the speed with which it hit the ground. Calculate
  1. the time taken for the stone to fall to the ground, [2 marks]
  2. the speed with which the stone hits the ground, [2 marks]
  3. the height to which the stone rises before it comes to instantaneous rest. [3 marks]
State two modelling assumptions that you have made. [2 marks]