Question

A punter wants to kick a football so that the football has a total flight time of 3.7 s and lands 56m away (measured along the ground). Neglect drag and the initial height of the football. What height will the football reach?

Answer 1

The maximum height is 16.8 m

Explanation:

In order to find the maximum height reached by the football, we can just analyze its vertical motion.

The vertical motion of the ball is a free  fall motion, affected only by the force of gravity. So it is a uniformly accelerated motion, and we can use suvat equations.

First of all, we notice that the motion of the ball is symmetrical, so the time taken to reach the maximum height is equal to the time needed to fall down: Since the total time of flight is

T = 3.7 s

It means that the time to reach the maximum height is

$t=\frac{T}{2}=\frac{3.7}{2}=1.85 s$

We can now find the maximum height reached using the equation:

$s=vt-\frac{1}{2}at^2$

Where:

s is the vertical displacement (the maximum height)

v = 0 is the velocity of the ball at the maximum height

t = 1.85 s is the time

$a=g=-9.8 m/s^2$ is the acceleration of gravity

Solving for s,

$s=-\frac{1}{2}(-9.8)(1.85)^2=16.8 m$

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