A ball is hit at a height 4 feet off the ground with an init

A ball is hit at a height 4 feet off the ground with an initial velocity of 135 feet/second. The ball leaves the bat at an angle of twenty-five degrees to the horizontal. What is the height of the ball after 3 seconds? How far has the ball traveled after three seconds? What is the maximum height of the ball? How long is the ball in the air? A 20 foot wall stands 400 feet from the batter; will the ball clear the wall?

Solution

Initial velocity = 135 ft/sec

Angle with hor = 25 degrees

Velocity along vertical = 135 sin 25 = 57.0535 ft/sec

a) s = ut+1/2 at^2+4

= 57.0535t-16t^2+4

When t=3

Hence h = 57.0535(3) -32/2 (9)+4

= 31.1605

b) Distance travelled = 135(3) -16(9)

= 261 ft/sec

c) h = 57.0535t-16t^2+4

h\' = 57.0535 -32t

h\' =0 when t = 1.783

maximum height = 54.857

d) Ball is in the air till h = -4

57.0535t-16t^2 = 0

t = 3.565