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Aero Pump/Kick $4.92 ...

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At what height is the speed of the ball equal to half of its initial value?

A ball is thrown straight up and rises to a maximum height of 23 m above the ground. At what height is the speed of the ball equal to half of its initial value? Assume that the ball starts at a height of 1.6 m above the ground.

Vf^2 = Vo^2 + 2ad
The velocity at the top of the trajectory is 0 m/s.
So Vf^2 = 0.
You know a and d so solve for Vo.
Vo = sqrt(-2ad)
Vo = 20.48 m/s; where d=23m-1.6m
You want to know where the velocity is 10.240 m/s. half of your Vo
Vf^2 = Vo^2 + 2ad
Vf = 10.24 m/s
Vo = 20.48 m/s
Solve for d and you get Vf^2-Vo^2/2a = d.
d = (103.84-415.34)/2(-9.8)+1.6m
d = 17.65m