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A baseball player hits a home run over the left-field fence, which is 104m from the home plate. The ball is hit at a point 1.00m directly above home plate, with an initial velocity directed 30.0 degrees above the horizontal. By what distance does the ball clear the 3.00m high fence if it passes over it 3.00s after being hit.

Verified Answer :

scme1702

Horizontal velocity of the ball:
104 / 3
= 34.7 m/s
Vx = Vcos(∅)
V = 34.7 / cos(30)
V = 40.1 m/s

Vertical velocity of ball:
Vy = 40.1 sin(30)
Vy = 20.1 m/s

The height of the ball at time t:
s = 20.1t - 1/2 x 9.8t² + 1; we add 1 because that is its initial height at t = 0
After 3 seconds, the height is:
s = 20.1(3) - 4.9(3)² + 1
s = 17.2 meters

The ball clears the 3 meter high fence by:
17.2 - 3
= 14.2 meters

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