Question

A football is kicked from the ground with an initial speed of 16 ms–1 at an angle of 24° to the horizon. At what two times will the ball have a height of 1.0 m? Assume the kick happens at t = 0 s.

Answer 1

A football is kicked from the ground with an initial speed of 16 m/s at an angle of 24° to the horizon. assuming the kick happens at t = 0 s.

To find : At what two times will the ball have a height of 1 m.

solution : vertical component of velocity, $u_y$ = 16sin24° ≈ 6.5

acceleration along vertical direction, $a_y$ = -g = -10 m/s²

displacement in vertical direction, y = 1 m

using formula, $y=u_yt+\frac{1}{2}a_yt^2$

⇒1 = 6.5t + 1/2 × (-10)t²

⇒5t² - 6.5t + 1 = 0

⇒t = {6.5 ± √(6.5² - 20)}/10

= {6.5 ± √(22.25)}/10

= 0.65 ± 0.47

= 0.18, 1.12

Therefore at 0.18s and 1.12 sec, football will have a height of 1m.