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.

Expert Answers
justaguide eNotes educator| Certified Educator

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.