Question

Mike Trout crushes a Jon Lester fastball towards right field. The ball is hit 1.00 m above the plate and its inital velocity is 36.5m/s at an angle of 30 degrees above the horizontal. The right field wall is 113m from home plate and the right field fence is 3 meters high

. How long does it take for the ball to reach the wall?

Does Mike Trout hit a home run? Prove your answer...

Answer 1

When the ball reaches the right field wall,

displacement in the x-direction = d = 113 m

velocity in the x-direction = ucosθ = 36.5*(cos30) = 36.5*(√3/2) = 31.61 m/s

acceleration in the x-direction = 0

d = (ucosθ)t

=> t = d/ucosθ = 113/31.61

=> t = 3.57 sec

Therefore, the time taken by the ball to reach the right field wall is 3.57 seconds.

let y be the displacement of the ball in the y-direction when it reaches the wall

s = ut + (1/2)at²

=> y = (usinθ)(t) + (1/2)(-9.81)(t²)

=> y = (36.5*sin30)(3.57) + (1/2)(-9.81)(3.57²)

=> y = 2.64 m

Initially, the ball was hit 1m above the plate(ground).

Therefore, height of the ball when it reaches the wall = 1+y = 1+2.64 = 3.64 m

Hence, the ball will clear the right field fence which is 3m high.

So, Mike trout has hit a home run