Answer:
144 ft
Step-by-step explanation:
The speed decreases linearly by 32 ft/sec/sec, so will be zero after ...
(96 ft/s)/(32 ft/s²) = 3 s
The average speed over that period is half the initial speed, so the distance covered between the ground and the maximum height is ...
(3 s)(96 ft/s)/2 = 144 ft
_____
Alternate solution
The relationship between velocity and distance for a constant acceleration is ...
[tex]v_f^{2}- v_i^{2} = 2ad[/tex]
For an initial velocity of 96 ft/s, a final velocity (at the top of travel) of 0, and the given acceleration, we have ...
[tex]d = \dfrac{v_f^{2}- v_i^{2}}{2a} = \dfrac{0-96^{2}}{2(-32)}= 144\,\dots\ \text{ft}[/tex]
