A golf ball is hit at ground level. The ball is observed to reach its maximum height 6.3 s after being hit. 0.97 seconds after reaching this maximum height, the ball barely clears a fence that is...

A golf ball is hit at ground level. The ball is observed to reach its maximum height 6.3 s after being hit. 0.97 seconds after reaching this maximum height, the ball barely clears a fence that is 410 ft away from where the ball was hit. How high is the fence?

The acceleration of gravity is 32 ft/s^2.

Asked on by cchsiao787

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The ball is struck when it is at ground level and it reaches the highest point after 6.3 seconds.

If the ball was struck with a velocity V at an angle A with the horizontal, the vertical component of the velocity is V*sin A. This reduces to 0 when the ball is at the highest point.

V*sin A - 32*6.3 = 0

V*sin A = 32*6.3

The maximum height is V*sin A*6.3 - 0.5*32*6.3^2

=> 32*6.3^2 - 0.5*32*6.3^2

=> 635.04 feet

The ball crosses the fence 0.97 seconds after it reaches the highest point. At this moment the height of the ball is 635.04 - 0.5*32*0.97^2

=> 635.04 - 15.0544 = 619.9856

The height of the fence is 619.9856 feet.

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