2. Pitching (6 points) On a baseball diamond, the pitcher\'s mound is a horizont

Question

2. Pitching (6 points) On a baseball diamond, the pitcher's mound is a horizontal distance of 18.3 m from home plate. LIU ace pitcher and physics major Cory Hart pitcher throws a baseball with an initial velocity of 40.0 m/'s horizontally. The ball is thrown from a height of 1.70 m above home plate. (Assume that air resistance can be neglected.) (a)(3 points) How long does it take for the ball to reach the batter at home plate? (3 points) When the ball reaches home plate, how high off the ground is it?

Explanation / Answer

given

horizontal distance from the pitcher to the home plate is 18.3 m

initial velocity of the baseball , pitcher can throw with respect to horizontal is 40 m/s

from a height h1= 1.70 m above the plate

using equations of motions  

we can treat it as an example of Horizontal projectile  

the time taken to reach the home plate is  

a)

X = U*t

t = X/u = 18.3/40 s = 0.4575 s

as we know along horizontal there is no change in velocity of the projectile  

b) using equations of motions  

s = ut +0.5 at^2

h1-h2 = u*t - 0.5*g*t^2

1.7-h2 = 40*0.4575 - 0.5*9.8*0.4575^2

h2 = -15.57 m

so height is 18.3- 15.57 = 2.73 m

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