# Physics

Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176 ft/s) at an angle of θ = 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?

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1. The ball's horizontal speed is 176 cos35° = 144 ft/s
So, it would take 565/144 = 3.92 seconds to travel to the wall.

The height of the ball is
y = 3 + 176 sin35° t - 16t^2
= 3 + 101t - 16t^2
So, what is y when t = 3.92?

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