University Physics: Force Problem (Baseball and Pitcher)

[BlueLava]

Homework Statement

A baseball with mass of m= 145g leaves a pitchers hand with a velocity of Vi = 46m/s.
If the pitchers arm moves through an angle of θ = 115◦, making an arch with radius of r= 55cm,what is the average force applied to the ball by the pitcher while she is throwing the ball? Note ,You can use the equation s = r θ for arclength as long as θ is in radians.

Relevant Equations

Average Force : F = m * (Vf – Vi) / t
Arclength : s = r θ

I've gone about getting the arclength S = 1.103m
The formula for average force is F = m * (Vf – Vi) / t
I know the mass and the initial velocity, but I don't know where arclength comes into play. I'm assuming Vf and T is referring to the moment that the ball leaves the pitchers hand, but I don't know how to go about solving those either.

 

[haruspex]

The question is flawed. As you say, the definition of average force is change in momentum divided by elapsed time.
The questioner expects you to use work = force x distance, but that is only sure to yield the same answer if the force is constant. So the question should be "what is the magnitude of the force, assuming it is constant ?"

Rather a serious blunder for a question at university level.

Edits above: corrected "sane" to "same" and inserted "magnitude".

 

[BlueLava]

The question is flawed. As you say, the definition of average force is change in momentum divided by elapsed time.
The questioner expects you to use work = force x distance, but that is only sure to yield the sane answer if the force is constant. So the question should be "what is the force, assuming it is constant ?"

Rather a serious blunder for a question at university level.

Thanks for the reply, my next question on the HW is
Air resistance takes 37 J of energy out of the ball, slowing it down while as it is moves between the pitcher and the catcher. What is the velocity of the ball just before it hits the catchers glove?
He gives us 0 info on the catcher, is this even solvable?

 

[kuruman]

Continuing the mind-reading process that @haruspex started, the questioner probably meant to ask you to find the speed (a scalar) not the velocity (a vector). Even so, you are correct in surmising that additional information on the catcher is needed, namely the vertical change of the ball's position when the ball is caught.

 

[haruspex]

Continuing the mind-reading process that @haruspex started, the questioner probably meant to ask you to find the speed (a scalar) not the velocity (a vector). Even so, you are correct in surmising that additional information on the catcher is needed, namely the vertical change of the ball's position when the ball is caught.

The speed ("velocity") is given, but you make an important point. We could assume the torque on the arm is constant, leading to constant angular acceleration. This would allow us to find the elapsed time. But now the question is whether the answer sought is the (constant) magnitude of the force or the magnitude of the average force as a vector! Surely it is the former.

Wrt catcher, that is irrelevant. It gives the speed on leaving the pitcher's hand.
The height unknown is in regard to change of height during the pitching arc.

 

[PeroK]

It's not exactly a major league question, if you ask me!