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Kicking a Ball Off the Boardwalk

A boy kicks a ball horizontally near the edge of a boardwalk, with an initial
speed of 9.0 m/s. A blowing wind gives the ball a constant horizontal
acceleration of 12 m/s^2.
The ball falls into the water directly under the boy.
Ignore the effect of air resistance on the vertical motion of the ball.

a. Determine the height of the boardwalk above water.

b.If the blowing wind reverses direction while maintaining the same
strength, where does the ball fall when it is kicked with the same
initial speed?

Solution Preview

a. By symmetry, the final horizontal velocity of the ball must be equal and opposite to its initial horizontal velocity. Thus we have

v_h(T) = v_h(0) - a_h T,

whence

-9.0 = 9.0 - 12 T,

so

0 = 18.0 - 12 T,

whence

T = 18.0 / 12 = 1.5 ...

Solution Summary

We analyze the motion of a ball being kicked off a boardwalk with a horizontal wind blowing either in the direction of the kick or in the opposite direction.

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