What Determines the Velocity of a Baseball After Being Hit?

[eiktmywib]

Homework Statement

My question is:
Now assume that the pitcher in Part D throws a 0.145 kg baseball parallel to the ground with a speed of 32 m/s in the +x direction. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. What is the ball's velocity just after leaving the bat if the bat applies an impulse of -8.4 N*s to the baseball?

Homework Equations

The first part of the question is this:
Assume that a pitcher throws a baseball so that it travels in a straight line parallel to the ground. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. Define the direction the pitcher originally throws the ball as the +x direction.
The right answer (that I got correct) is this:
The impulse on the ball caused by the bat will be in the negative x direction.

The Attempt at a Solution

Well I know that impulse is just the change in momentum...
So I did
mv=mv
8.4 N*s=(0.145)(v)
and I got 57.9 m/s... which was wrong

AND ONE MORE QUESTION PLEASE...

Homework Statement

My question is:
Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 10.9 m/s. Olaf's mass is 73.5 kg.
If the ball hits Olaf and bounces off his chest horizontally at 7.30 m/s in the opposite direction, what is his speed vf after the collision?

Homework Equations

The first part of the question is:
If Olaf catches the ball, with what speed v_f do Olaf and the ball move afterward?
I got 5.90 cm/s, which is right.

The Attempt at a Solution

I found the initial momentum which is (-7.3 m/s * 100cm/1m)(0.400 kg) = -292 kgcm/s
And this was right

And then I tried momentum final = mv
-292 = (73.5kg)(v)
And it was wrong...

 

[jamesrc]

For the first problem: Impulse is equal to the change in momentum, not the momentum...

For the second problem: I don't see you trying to set up the problem correctly. Initially, the momentum of the system is all in the ball (that momentum would be equal to the mass of the ball times the velocity of the ball). After the collision, both the ball and Olaf are moving, so the total momentum would be the sum of the ball's momentum (its mass times velocity) and Olaf's (his mass times velocity; his velocity is what you are solving for).

 

[thomate1]

I would like to point out some misconceptions in your attempts at solving these problems.

Firstly, impulse is not just the change in momentum. It is defined as the force applied over a certain time interval, which results in a change in momentum. In the first problem, the impulse applied by the bat is given as -8.4 N*s, which means that the force applied by the bat is in the negative x direction and acts for a duration of 8.4 seconds. Therefore, your equation of mv=mv is incorrect. The correct equation to use in this scenario is FΔt=Δp, where F is the force, Δt is the time interval, and Δp is the change in momentum. So, using this equation, we get (-8.4 N)(8.4 s) = (0.145 kg)(v), which gives us a final velocity of -48.3 m/s in the negative x direction.

Secondly, in the second problem, you have used the wrong units for momentum. The unit for momentum is kg*m/s, not kgcm/s. Therefore, the correct initial momentum should be -292 kg*m/s. Also, in your attempt at solving for the final velocity, you have used the wrong equation. The correct equation to use in this scenario is m1v1 + m2v2 = m1v1' + m2v2', where m1 and m2 are the masses of Olaf and the ball respectively, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities. Plugging in the values, we get (73.5 kg)(0 m/s) + (0.400 kg)(-7.3 m/s) = (73.5 kg)(v) + (0.400 kg)(7.3 m/s), which gives us a final velocity of -0.05 m/s, or essentially 0 m/s. This means that Olaf and the ball would come to a stop after the collision.

To summarize, it is important to understand the concepts of momentum and impulse correctly and use the appropriate equations when solving problems. It is also important to pay attention to units and use them correctly in calculations.