Baseball Hitting Physics

baseball hitting physics




Baseball Physics?

A baseball is hit at an initial velocity of 110 ft/s at an angle of 45 degrees above the horizontal. Will the ball clear a 10.0 ft fence 300 ft from home plate for a home run? If so, by how much will it clear the fence? If not, how far in front of the fence will it land or where will it hit the wall?

Let:
x be the horizontal distance at time t,
y be the height at time t.

x = 110t cos(45)
t = x / 110 cos(45)

y = 110t sin(45) – 32t^2 / 2

Eliminating t:
y = x – 32x^2 / [ 2 * 110^2 cos^2(45) ]

Putting x = 300ft:
y = 300 – [ 300 / 110 cos(45) ]^2 * 16
= 62.0 ft.

The ball will clear the fence by 62 – 10 = 52ft.

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