A cricket ball 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?
A)8.2 m
B)15.8 m
C)13.5 m
D)11.0 m
E)4.9 m

Question

Quizplus · Accepted Answer

Using kinematic equations, we can find that the maximum height reached by the ball above ground level is h = 11.025 m. 
Then, we can use the equation for horizontal distance traveled: 
d = v0xt 
where v0x is the initial horizontal velocity (which is constant throughout the motion), and t is the total time of flight (which we can find as 2 times the time it takes to reach maximum height). 
Rearranging and solving for v0x: 
v0x = d/t = 97.5 m / (2 x 6.0 s) = 8.125 m/s 
Finally, we can use the kinematic equation for vertical displacement with constant acceleration (ignoring air resistance) to find the height of the fence: 
hf = hi + v0it - (1/2)gt^2 
where hi is the initial vertical position (which is zero), v0i is the initial vertical velocity (which is also zero), and g is the acceleration due to gravity (which is -9.81 m/s^2). 
Plugging in the values for t and v0i: 
hf = 11.025 m + (8.125 m/s)(2.5 s) - (1/2)(9.81 m/s^2)(2.5 s)^2 
hf = 13.5 m

A Cricket Ball Is Hit at Ground Level