Calculating Impulse Force for a Pitched Ball: How to Find the Final Velocity?

[lab-rat]

Homework Statement

A fast ball is pitched at a batter who hits a pop fly vertically into the air. The ball was moving horizontally at 38.45 m/s when it was hit by the bat. As it left the bat it was moving vertically and reached a maximum height of 44.196m. The mass of a baseball is 0.1417 kg. If the ball was in contact with the bat for 3/1000 of a second, determine the magnitude and direction of the impulse force with which it was struck.


I need to find the change in momentum. So I need to find the initial and final velocity. The only thing left that I can't do is find the final velocity. How do I calculate it when all that I know is the vertical height?

 

[PeterO]

Homework Statement

A fast ball is pitched at a batter who hits a pop fly vertically into the air. The ball was moving horizontally at 38.45 m/s when it was hit by the bat. As it left the bat it was moving vertically and reached a maximum height of 44.196m. The mass of a baseball is 0.1417 kg. If the ball was in contact with the bat for 3/1000 of a second, determine the magnitude and direction of the impulse force with which it was struck.


I need to find the change in momentum. So I need to find the initial and final velocity. The only thing left that I can't do is find the final velocity. How do I calculate it when all that I know is the vertical height?

For vertical motion, there is a constant downwards acceleration of g [we are told to take g= 9.8, 9.81 or 10 depending what level Physics you are taking]

From that , and the height reached, you can calculate the initial velocity.

 

[lab-rat]

but I don't have the time and the formula is v=vo + at

 

[lab-rat]

or s=vot + a(1/2 a) t2

 

[PeterO]

or s=volt + a(1/2 a) t2

ever heard of V² = V_o² + 2as

 

[lab-rat]

OK, but the acceleration would be negative, so how can I find the square root?

 

[PeterO]

OK, but the acceleration would be negative, so how can I find the square root?

Yes, it is negative, but you have to move it to the other side of the equation [whence it will become positive] since you are trying to find V_o.

V = 0 because it has finally stopped going up when it reaches maximum height.

 

[lab-rat]

Ohh, I thought I was looking for V. Vo = 29.43 j m/s

So I found Pi= 5.448i kgm/s
and Pf= 4.17j kgm/s

I need to find the change in momentum so Pf-Pi, how do I go about subtracting those vectors?

 

[PeterO]

Ohh, I thought I was looking for V. Vo = 29.43 j m/s

So I found Pi= 5.448i kgm/s
and Pf= 4.17j kgm/s

I need to find the change in momentum so Pf-Pi, how do I go about subtracting those vectors?

A pythagorus solution is what you are after.

The change in momentum has to get rid of a lot of horizontal momentum, and produce a lot of vertical momentum at the same time, so it will have an up component, and a "back towards the pitcher" component

 

[lab-rat]

So Vo is 29.43 m/s, and the back towards pitcher component is -29.43 m/s correct?

And I would just need to find the horizontal velocity ?

 

[PeterO]

So Vo is 29.43 m/s, and the back towards pitcher component is -29.43 m/s correct?

And I would just need to find the horizontal velocity ?

No. The ball arrived at 38+ m/s, then went up at 29+ m/s, so the change is 38+ back, and 29+ up.

 

[lab-rat]

OK, so what would the variation of momentum be ?

P = mv

I have (4.17 j - 5.45 i) kgm/s But my problem is that I can't subtract j's and i's.

I need either two horizontal vectors or two vertical vectors

Then I just need to divide the change in momentum by 3/1000

 

[lab-rat]

OK so I used the pythagorea theorem but that gave me the resulting momentum when I only need the difference in momentum.

It's probably really simple, I'm just not seeing it right now...

 

[lab-rat]

I ended up just doing (4.17j-5.448i) / 3/1000
Fnet=(1390j-1816i) N

does that work?

 

[PeterO]

I ended up just doing (4.17j-5.448i) / 3/1000
Fnet=(1390j-1816i) N

does that work?

NO.

This question is basically a test of whether you can add and subtract vectors. Looks like you can't.
It is done by drawing arrows which forms triangles which you use trigonometry and/or pythagorus to solve. Google search if you can't find it in your own text.

 

[PeterO]

OK, so what would the variation of momentum be ?

P = mv

I have (4.17 j - 5.45 i) kgm/s But my problem is that I can't subtract j's and i's.

I need either two horizontal vectors or two vertical vectors

Then I just need to divide the change in momentum by 3/1000

The bit I highlighted is a real problem. You have to learn how to do that.

 

[lab-rat]

I actually do know how to subtract vectors, but my professor had said that we did not have time to cover that section, so we wouldn't see vector addition/subtraction.
So I assumed we wouldn't have any assignments on it, and thought there was another way to do this problem.

Anyways, I ended up doing it anyway and found 2286.57N (N52.6degresW)