Professional pitchers in the major leagues are known to accelerate a baseball with a mass of 140 g from rest to a velocity of 95 mph over a distance of 2 m before releasing it. (1 mph = 0.447 m/s)
a. Assuming that the force exerted on the ball by the pitcher is constant, determine the force necessary to throw a fast ball
b. Determine the amount of time required for the ball to travel a distance of 20 m to the catcher's mitt (neglect air resistance and approximate as constant velocity motion)
c. Once the catcher's mitt has made contact with the ball, the ball travels 4 cm into the mitt before coming to rest. Determine the force exerted on the ball by the mitt during this interaction, and describe what the sign indicates
d. Determine the force exerted on the mitt by the ball during this interval, and describe what the sign indicates
e. Equipped with Newton's Laws and the kinematic equations, explain why most of the fastest pictures in the major leagues are tall (they have long arms and legs)
f. If a much shorter pitcher accelerates the ball to 95 mph in half the distance that a much taller pitcher uses, by what factor does the force exerted on the ball by the pitcher's hand have to increase by?
Answers & Comments
Verified answer
Too many questions in one post. Chances of getting all the answers are slim.
a) a = (Vf^2 - Vi^2) / 2d = 450 m/s^2 F = ma = 63 N
b) t = d/v = 0.47 s
c) F = - 3.16x10^4 N (see the solution for "a"). Negative sign indicate, the force opposes the motion of the ball (slows the ball down)
You can answer the rest, using the same formulas.