Question

Jade, a pro softball player, hits the ball when it is 3 feet off the ground with an initial velocity of 100 ft/sec and at an angle of 35° from the horizon. A straight line wind is blowing at 14 ft/sec in the direction the ball is traveling.

She hits the ball towards a 40-foot fence that is 120 feet from the plate; if it clears the fence, the ball is a home run.

(a) Will the hit be a home run?
(b) If so, how much does it clear the fence? If not, how much does it miss the fence?

Answer 1

The horizontal component of the velocity of the ball will be 100 cos 35 + 14
= 95.92 ft/sec.
The time for the ball to reach the fence = 120 / 95.92 = 1.251 seconds.
We now have to find the height of the ball after 1.251 seconds.
Vertical component of the velocity = 100 sin 35 = 57.36 ft/second
It has to be at a height of over 40 ft at time 1.251 seconds.

equation of motion is h = 57.36t - 16t^2 + 3

so we have h = 57.36(1.251) - 16(1.251)^2 + 3 = 49.7 feet
so (a) it will be a home run and
(b) it clears the fence by 9.7 feet.