Ted Williams, Professor Emeritus of Hitting with the Boston Red Sox, visits the

Question

Ted Williams, Professor Emeritus of Hitting with the Boston Red Sox, visits the Skydome in Toronto where all distances are measured in meters. He demonstrates to the younger Bluejays how it is done by hitting a home run that clears a low fence 119 m from home plate.

c) When the ball is hit with the speed and angle determined above, how long does it take the ball to travel the distance to the fence?

d) For these same conditions, find the maximum height (relative to the top of the fence) reached by the ball on its trajectory.

Explanation / Answer

X direction There is no external force acting on the ball in the X direction since the ball goes horizontally, and air resistance is not included. SO the initial and final velocities must be the same, as teh ball covered teh 120m HORIZONTAL distance to the fence v1=v2=v0 cos 45 a=0 d = 120 d = vt = 120 = (v0 cos 45) t..........(1) The ball was initially thrown upward with a component pointing straight up. When the ball reaches the fence it has now COMPLETELY reversed direction. If i took the upward to be positive then the down must be negative Hence Y direction v1=v0 sin45 v2=-v0 sin45 a= -9.8m/s^2 t=? v2 = v1 + at v0 sin45 = -v0 sin45 - 9.8t t = 2v0 sin45 / 9.8 ......... (2) substitute 2 in to 1 120 = (v0 cos 45) (2v0 sin 45 / 9.8) and solve for v0 to find the time taken, well you know the velocity now, so sub it into 2 or 1 and solve for t To find the maximum height ask yourself what is the velocity VERTICAL ONLY when the ball has reached its maximum height? you know v1, v2, a (well something happened to the speed so there must a force acting) and solve for t using v2 = v1 + at

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