The fastest pitched baseball was clocked at 47 m/s. assume that the pitcher exerted his force (assumed to be horizontal and constant) over a distance of 1.0 m, and a baseball has a mass of 145 g. a) draw a free-body diagram of the ball during the pitch. the ball is moving to the right.
b) what force did the pitcher exert on the ball during this record-setting pitch?
c) estimate the force in part b as a fraction of the pitcher’s weight. assume that the pitcher has a mass of 84 kg.

The force the pitcher exert on the ball during this record-setting pitch is 160.15 N.

The force exerted on the baseball as a fraction of the pitcher's weight is 0.195.

The given parameters;

The free-body diagram of the ball during the pitch is in the image added.

The acceleration of the baseball over the given distance is calculated as;

v² = u² - 2as

when the ball stops, the final velocity, v = 0

0 = u² - 2as

2as = u²

The force the pitcher exert on the ball during this record-setting pitch is calculated as;

F = ma

F = 0.145 x 1,104.5

F = 160.15 N.

The weight of the pitcher is calculated as;

W = mg

W = 84 x 9.8

W = 823.2 N

The force exerted on the baseball as a fraction of the pitcher's weight is calculated as follows;

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A) In attachment

Find the free-body diagram in attachment. There are only two forces acting on the ball during the pitch:

- The force applied by the pitcher, F, which acts in the horizontal direction

- The force of gravity acting on the ball, also called weight, whose magnitude is

where m is the mass and g is the acceleration of gravity, and it acts in the downward direction.

B) 160.2 N

First of all, we need to find the acceleration of the ball. We can do it by using the SUVAT equation

where

v = 47 m/s is the final velocity of the ball

u = 0 is the initial velocity (the ball starts from rest)

a is the acceleration

d = 1.0 m is the distance covered by the ball while the force is applied

Solving for a,

And since we know the mass of the ball,

m = 145 g = 0.145 kg

We can find the force exerted on it by using Newton's second law:

C) 0.195 times the pitcher's weight

The weight of the pitcher is given by

W = mg

where

m = 84 kg is the mass of the pitcher

g = 9.8 m/s^2 is the acceleration of gravity

Solving,

So now we can express the force found in part B) as a fraction of the pitcher's weight:

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it about 600 mph from what i calculated