In a penalty kick in soccer, the ball is placed on the ground 11 m from the goal

Question

In a penalty kick in soccer, the ball is placed on the ground 11 m from the goal. The height of ball when it reaches the goal must be less than 2.4 m to enter the net (the goal post is officially 2.44 m from the ground), and the kicker knows that the goalkeeper (goalie) will be able to block the kick if the ball’s height at the net is less than 2.0 m. The kicker is trying to remember what he learned in PHYS 1020, and decides to kick the ball with an initial speed of 30 m/s at an angle of 15° with respect to the ground. You may assume that his kick arrives within the width of the goal (i.e., does not miss to the left or to the right of the net) and that air resistance is negligible. Which of the following possible answers is correct?

Explanation / Answer

Time taken to reach goal post = t = 11/30 cos 15 = 0.38 s

Vy=30 sin 15 = 7.76 m/s

Height of ball in 0.38 s = h = 7.76* 0.38 - 0.5*9.8*0.38^2 = 2.4124 m

Ball reaches the goal post at a height of 2.4124 m

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