Abaseball is hit at ground level. the ball is observed to reach its maximum height above ground level 3.0 s after being hit. and 2.5 s after reaching this maximum height, the ball is observed to barely clear a fence that is 97.5 m from where it was hit. how high is the fence?

y= 13.475 m

Explanation:

 Kinematics of the ball : The ball describes a parabolic trajectory.

Because ball move with uniformly accelerated movement in y we apply the following formulas:

 Formula (1)

 Formula (2)

Where:  

y :  vertical position for any time t  (m)  

y₀ : Initial vertical position   (m)

t :    time in seconds (s)

     : Initial speed in y (m/s)  

     : Final speed in y (m/s)

g: acceleration due to gravity (m/s)²

Problem development

We apply formula 1 when the ball reaches its maximum height to obtain the initial velocity at y,  :

at maximum height : t= 3 s,    = 0

We calculate the requested height using formula 2

t= 3s+2.5s = 5.5 s, , y₀ = 0

y=13.475 m