Mechanics A Level Maths Worksheets, Questions and Revision

A ball is thrown vertically upwards from ground level with initial speed 14 m/s, and is modelled as a particle moving freely under gravity with g = 9.8 m/s^2. (a) Find the greatest height reached by the ball. (b) Find the total time the ball is in the air before it returns to ground level.

1. Taking upwards as positive, at the greatest height v = 0, u = 14, a = -9.8. Use v^2 = u^2 + 2as: 0 = 14^2 + 2(-9.8)s.
2. 0 = 196 - 19.6s, so s = 196/19.6 = 10 m.
3. For the total time in the air, use s = 0 (the ball returns to its starting height) in s = ut + (1/2)at^2: 0 = 14t - 4.9t^2.
4. Factorise: 0 = t(14 - 4.9t), giving t = 0 (the start) or t = 14/4.9 = 2.857... s.
5. Round the non-zero solution to 3 significant figures: t = 2.86 s.