Question

A punter kicks a football from the ground with a velocity of 19 m/s at an angle 32 degrees from the horizontal the football travels a horizontal distance of 33m before it hits the ground what is the maximum height the football reaches

Answer 1

Answer: 5.17 m

Step-by-step explanation:

The football reaches its maximum height when the vertical component of the velocity is zero:

`V_(y)=0 m/s`

This is exactly at the point where the football stops and then begins to fall thanks to the acceleration due gravity.

So, we can use the following equation:

`(V_(y))^(2)=(V_(oy))^(2)-2gy_(max)`

Where:

`V_(y)=0` is the final velocity

`V_(oy)=V_(o) sin(32\°)` is the vertical component of the initial velocity

`V_(o)=19 m/s` is the initial velocity

`g=9.8 m/s^(2)` is the acceleration due gravity

`y_(max)` is the football's maximum height

Isolating
`y_(max)`:

`y_(max)=((V_(o) sin(32\°))^(2))/(2g)`

`y_(max)=((19 m/s sin(32\°))^(2))/(2(9.8 m/s^(2)))`

Finally:

`y_(max)=5.17 m` This is the football's maximum height