Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176

Question

Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176 ft/s) at an angle of ? = 35 degrees to the horizontal. The ball is struck 3 feet above home plate. You watch as the ball goes over the outfield wall 420 feet away and lands in the bleachers. After you congratulate Ted on his hit he tells you, 'You think that was something, if there was no air resistance I could have hit that ball clear out of the stadium!'

Assuming Ted is correct, what is the maximum height of the stadium at its back wall x = 565 feet from home plate, such that the ball would just pass over it? You may need:

•9.8 m/s2 = 32.2 ft/s2
•1 mile = 5280 ft

Explanation / Answer

Shift the origin to the point where Ted hits the ball. Now use the kinematics equation y = x tan? - gx2 / 2 (v cos?)2. y = 565* 0.700 - 32.2 * (565)2 / 2(176 * 0.8191)2 y = 395.5 - 32.2*7.8 y=395.5-251.16 y=144.34 feet But this is the height considering the point 3 feet above the ground. So the actual height above the ground = 144.34 + 3 =147.34 feet

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