In a baseball a pitcher can accelerate a .15kg ball from rest to 98 mi/h in a distance of 1.7m

a) what is the average force exerted on a ball during a pitch?
b)If the mass of the ball is increased, is the force required of the pitcher increased, decreased or unchanged?

Work is nice, but be careful with your decimal point. Check answer line.....

a. V=98mi/h * 1600m/mi * 1h/3600s.=43.6 m/s

V^2 = V0^2 + 2a*d.
a = (V^2-Vo^2)/2d.
a = (1897.1-0)/3.4 = 558 m/s^2.

F = m*a = 15 * 558 = 8370 N.

b. Increased.

a) Well, I'm not a fan of baseball, but I can certainly give you a silly answer! So, with my comical calculations, it seems that the average force exerted on the ball during a pitch is... drumroll, please... "a whole lot of oomph!" Yes, that's right, the pitcher needs to summon all their strength to propel that ball like a superstar!

b) Now, if the mass of the ball is increased, oh boy, things might get a bit trickier for our poor pitcher. Imagine trying to pitch a coconut instead of a baseball? So, to answer your question, the force required of the pitcher would likely increase. They'll have to summon even more oomph to get that heavier ball flying through the air!

Remember, these answers may be silly, but they should put a smile on your face!

a) To find the average force exerted on the ball during a pitch, we can use the equation:

Force = (mass * change in velocity) / time

First, let's convert the velocity from miles per hour (mi/h) to meters per second (m/s):

98 mi/h * (1.60934 km/h) * (1 m/1000 km) * (1 h/3600 s) = 43.8 m/s

Now we can calculate the average force:

Force = (0.15 kg * 43.8 m/s - 0 m/s) / 1.7 m

Force = 9.27 N

Therefore, the average force exerted on the ball during a pitch is approximately 9.27 Newtons.

b) If the mass of the ball is increased, the force required of the pitcher will increase. This is because according to Newton's second law of motion, force is directly proportional to mass and acceleration. If the mass increases, the force required to accelerate the ball to the same velocity will also increase.

To answer these questions, we need to use the principles of Newton's laws of motion and the equations of motion. Let's break it down step by step:

a) To find the average force exerted on the ball during the pitch, we can use the equation:

Average Force = (Change in momentum) / (Time taken)

First, let's find the change in momentum by using the following equation:

Momentum = Mass * Velocity

Given that the mass of the ball is 0.15 kg and the final velocity is 98 miles per hour (mi/h), we need to convert the velocity to meters per second (m/s). Since 1 mile = 1609.34 meters and 1 hour = 3600 seconds, the velocity in m/s will be:

Final Velocity = (98 * 1609.34) / 3600

Next, we calculate the initial velocity. Since the ball starts from rest, the initial velocity is 0 m/s.

Now, let's calculate the change in momentum:

Change in Momentum = (Mass * Final Velocity) - (Mass * Initial Velocity)
= (0.15 * Final Velocity) - (0.15 * 0)

Given the distance covered by the ball during the pitch is 1.7 m, we can calculate the time taken using the equation:

Distance = (Initial Velocity * Time) + (0.5 * Acceleration * Time^2)

Since the initial velocity is 0 m/s and the ball's motion is in a straight line, the equation simplifies to:

Distance = 0.5 * Acceleration * Time^2

Now we can solve for the time taken:

1.7 = 0.5 * (Acceleration) * (Time^2)

Solving this equation, we can find the value of acceleration.

Once we have the value of acceleration, we can calculate the average force by substituting the values into the first equation:

Average Force = (Change in Momentum) / (Time taken)

b) If the mass of the ball is increased, the force required of the pitcher would be increased. According to Newton's second law of motion, force is directly proportional to mass (F = ma). Therefore, if mass is increased, the force required to accelerate the ball to a certain velocity would also increase.