Vertical projection: speed of projection

A question is this type if and only if you must find the initial speed of projection given information about maximum height, time of flight, or final conditions.

6 questions · Moderate -0.8

3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form
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CAIE M1 2022 June Q2
5 marks Moderate -0.8
2 A particle \(P\) is projected vertically upwards from horizontal ground. \(P\) reaches a maximum height of 45 m . After reaching the ground, \(P\) comes to rest without rebounding.
  1. Find the speed at which \(P\) was projected.
  2. Find the total time for which the speed of \(P\) is at least \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Edexcel M1 2011 January Q2
8 marks Moderate -0.3
2. A ball is thrown vertically upwards with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point \(P\) at height \(h\) metres above the ground. The ball hits the ground 0.75 s later. The speed of the ball immediately before it hits the ground is \(6.45 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball is modelled as a particle.
  1. Show that \(u = 0.9\)
  2. Find the height above \(P\) to which the ball rises before it starts to fall towards the ground again.
  3. Find the value of \(h\).
Edexcel M1 2008 June Q2
7 marks Moderate -0.8
2. At time \(t = 0\), a particle is projected vertically upwards with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a point 10 m above the ground. At time \(T\) seconds, the particle hits the ground with speed \(17.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find
  1. the value of \(u\),
  2. the value of \(T\).
Edexcel M1 2009 January Q2
5 marks Moderate -0.8
2. A small ball is projected vertically upwards from ground level with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball takes 4 s to return to ground level.
  1. Draw, in the space below, a velocity-time graph to represent the motion of the ball during the first 4 s .
  2. The maximum height of the ball above the ground during the first 4 s is 19.6 m . Find the value of \(u\).
Edexcel M1 2003 November Q1
6 marks Easy -1.2
A small ball is projected vertically upwards from a point A. The greatest height reached by the ball is 40 m above A. Calculate
  1. the speed of projection. [3]
  2. the time between the instant that the ball is projected and the instant it returns to A. [3]
AQA AS Paper 1 2024 June Q16
3 marks Easy -1.2
In this question use \(g = 9.8\) m s\(^{-2}\) A ball is launched vertically upwards from the Earth's surface with velocity \(u\) m s\(^{-1}\) The ball reaches a maximum height of 15 metres. You may assume that air resistance can be ignored. Find the value of \(u\) [3 marks]