Question

Charlie Brown kicks a football at 20.5 m/s at 31.0°. It lands on flat ground 2.15 s later. How far away did it land? (Unit = m)

Answer 1

distance, x = 38.17 m

Given:

velocity of the football, v = 20.5 m/s

football projected at an angle,
`\theta = 30^(\circ)`

Period of flight, T = 2.15 s

Solution:

Since, the velocity is projected at some angle, so it can be resolved in horizontal and vertical components:

vertical component,
`u_(v) = usin\theta`

horizontal component,
`u_(h) = ucos\theta`

the component responsible to cover certain distance is
`u_(h) = ucos\theta`

Therefore, the distance covered by the football, x is given by:

`x = ucos\theta * T`

⇒
`x = 20.5cos30^(\circ)* 2.15`

x = 38.17 m