Question

A football is kicked from ground level with an initial velocity of 20.2 m/s at angle of 43.0 above the horizontal. How long, in seconds, is the football in the air before it hits the ground? Ignore air resistance. s

Answer 1

Given data

*The given initial velocity of the football is v = 20.2 m/s

*The angle above the horizontal is

`\theta=43.0^0`

*The value of the acceleration due to gravity is a = -9.8 m/s^2

The vertical component of the velocity is calculated as

`\begin{gathered} v_i=v\sin \theta \\ =(20.2)*\sin (43.0^0) \\ =13.77\text{ m/s} \end{gathered}`

The formula for the time required by the ball to reach the maximum height is given by the equation of motion as

`v_f=v_i+at`

*Here v_f = 0 m/s is the final velocity of the football at maximum height

Substitute the known values in the above expression as

`\begin{gathered} (0)_{}=13.77+(-9.8)(t) \\ t=1.40\text{ s} \end{gathered}`

The total time is taken by the football before it hits the ground is calculated as

`\begin{gathered} T=t+t \\ =1.40+1.40 \\ =2.80\text{ s} \end{gathered}`