Question

A baseball leaves the bat 1.5m above the ground traveling at 100mph at an angle of 27 degrees above the horizontal. There is a 3.1m high fence 14m a. Assuming air resistance is negligible on which side of the fence does the baseball first hit? b. How far from the fence does it first make impact?

Answer 1

Solution-

Use the equation of motion in X and Y direction,

For Y direction,

substitute,

ho = 1.5 m,

uy=100X0.45sin27 =20.43 m/s

(Note 1 mph = 0.447 m/s)

a=-g,

For X direction,

ux=100X0.45Xcos27=40.09 m/s

Fence coordinates are (14,3.1)

Find the time,

Use in y coordinate,

m

Therefore when ball is at x=14 m it has a height of 8.05 m (not 3.1) so it will not strike the fence.

The ball will strike at the ground after the fence(right side),

solve for t,

t = 4.24 s

Find X at t=4.24 s,

The distance from fence is 169.98-14 = 155.982 m

Answer-

(a) ball first strike after the fence on the ground at 169.98 distance from initial position,

(b) 155.982 m after the fence the ball will strike.