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

Answer:

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:

$x = ucos\theta \times T$

⇒  $x = 20.5cos30^{\circ}\times 2.15$

x = 38.17 m