Question

With what speed must a ball be thrown vertically from ground level to rise to a maximum height of 40 m? (b) How long will it be in the air?

Answer 1

The maximum height to which the body has been raised, h = 40 m

Acceleration due to gravity, g = 9.8 m/s2

Final velocity at the highest of point of reach, v = 0 m/s

Using the kinematic equation, V2 = U2 + 2gS,

0 = U2 - 2gh

U2 = 2gh = 2 x 9.8 x 40 = 784

U = 28 m/s

The speed with which the ball must be thrown vertically to reach a

maximum height is U = 28 m/s

Using the kinematic equation, V = U + at,

0 = U – gt

gt = U

t = u/g = 40/9.8 = 4.08 s

time taken to reach the maximum height, t = 4.08 s

from the maximum height, the ball will take exactly the same time to reach the ground back. The total time spend by the ball in air, T = 2t = 2 x 4.08 = 8.16 s