A football kicker is attempting a field goal from 44 m from the goal post. The ball is kicked and just clears the crossbar 2.9 s later. If the angle of the kick was 45°, what was the initial speed of the ball?

A. 39 m/s

B. 19.7 m/s

C. 2.2 m/s

D. 21.6 m/s

This problem is a projectile motion problem, where we know that the ball reaches a horizontal distance of x=44 m in a time of t=2.9 s. We also know that the ball was kicked with an angle of [tex]\theta=45^{\circ}[/tex].

We are only interested in the horizontal motion of the ball, which is a uniform motion with constant speed [tex]v_0 cos \theta[/tex], where [tex]v_0[/tex] is the initial speed of the ball. The horizontal velocity is simply equal to the ratio between the horizontal distance and the time:

[tex]v_0 cos \theta=\frac{x}{t}[/tex]

Re-arranging the equation, we find

[tex]v_0 = \frac{x}{t cos \theta}=\frac{44 m}{(2.9 s)( cos 45^{\circ})}=21.5 m/s[/tex]

So, the best answer is

D. 21.6 m/s

A football kicker is attempting a field goal from 44 m from the goal post. The ball is kicked and just clears the crossbar 2.9 s later. If the angle of the kick was 45°, what was the initial speed of the ball? A. 39 m/s B. 19.7 m/s C. 2.2 m/s D. 21.6 m/s

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A football kicker is attempting a field goal from 44 m from the goal post. The ball is kicked and just clears the crossbar 2.9 s later. If the angle of the kick was 45°, what was the initial speed of the ball?

A. 39 m/s

B. 19.7 m/s

C. 2.2 m/s

D. 21.6 m/s