During practice, a player P punts a ball B with a speed Vo=25 ft/s, at an angle

Question

During practice, a player P punts a ball B with a speed Vo=25 ft/s, at an angle theta = 60 degrees, and at a height h from the ground. Then the player sprints along a straight line and catches the ball at a same height from the ground. Then the player sprints along a straight line and catches the ball at the same height from the ground at which the ball was initally kicked. The length d denotes the horizontal distance between the player's position at the start of the sprint and the ball's position when the ball leaves the player's foot. Also, let delta t denote the time interval between the instant at which the ball leaves the players' foot and the instant at which the player starts sprinting. Assume d=0 and delta t =0, determine the average speed of the player so that he catches the ball.

Explanation / Answer

considering a normal projectile.

(Range of projectile = v^{2}*sin(2 heta)/g = 16.83 ft)

(Time-of-flight = 2*v*sin( heta)/g = 1.35 s)

so the player should also cover this linear distance in the same time to catch the ball.

( herefore speed = 16.83 / 1.35 = 12.47 ft/s)

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