Solving a Physics Problem: Boy & Girl on a Frozen Pond

[Mltn12]

Homework Statement

A 55-kg girl is standing near and to the left of a 75-kg boy on the frictionless surface of a frozen pond. The girl tosses a 1.8-kg ice ball to the girl with a horizontal speed of 7.5 m/s and he catches it. What are the velocities of the boy and the girl immediately after the boy catches the ball?

Homework Equations

MgVog+MbVb=0
Vfg=MballVb-Mb / Mg

The Attempt at a Solution

1.8kg x 7.5 m/s - 75kg / 55kg
= -1.1

Vfb=1/2 MbVb/ ( -1.1Mg-Mb)
= -10x10^-2

I don't think I did this correctly, can someone walk me through this?

 

[Nathanael]

Try solving it for only the girl. If a 55 kg girl throws a 1.8kg ball at 7.5 m/s what will be her final speed? (When she starts at rest)

 

[SammyS]

Homework Statement

A 55-kg girl is standing near and to the left of a 75-kg boy on the frictionless surface of a frozen pond. The girl tosses a 1.8-kg ice ball to the girl with a horizontal speed of 7.5 m/s and he catches it. What are the velocities of the boy and the girl immediately after the boy catches the ball?

Homework Equations

MgVog+MbVb=0
Vfg=MballVb-Mb / Mg

The Attempt at a Solution

1.8kg x 7.5 m/s - 75kg / 55kg
= -1.1

Vfb=1/2 MbVb/ ( -1.1Mg-Mb)
= -10x10^-2

I don't think I did this correctly, can someone walk me through this?

Hello Mltn12. Welcome to PF !

 

[Mltn12]

V=Vo+at?
A=t/v, but I don't have t.

 

[Mltn12]

Try solving it for only the girl. If a 55 kg girl throws a 1.8kg ball at 7.5 m/s what will be her final speed? (When she starts at rest)

V=Vo+at?
A=t/v, but I don't have t.

 

[Nathanael]

Homework Equations

MgVog+MbVb=0

What about this equation? That is conservation of momentum, right? Shouldn't it also apply to the girl and the ball?

 

[Mltn12]

What about this equation? That is conservation of momentum, right? Shouldn't it also apply to the girl and the ball?

Vfg=MballVb-Mb / Mg

1.8kg x 7.5 m/s - 75kg / 55kg
= -1.1

 

[Nathanael]

Vfg=MballVb-Mb / Mg

1.8kg x 7.5 m/s - 75kg / 55kg
= -1.1

Where did you get $V_{girl}=M_{ball}V_{ball}-\frac{M_{ball}}{M_{girl}}$?

Use the other equation $M_{girl}V_{girl}+M_{ball}V_{ball}=0$

 

[Mltn12]

Where did you get $V_{girl}=M_{ball}V_{ball}-\frac{M_{ball}}{M_{girl}}$?

Use the other equation $M_{girl}V_{girl}+M_{ball}V_{ball}=0$

(1.8 kg)( 7.5 m/s) / (55kg)
.25 m/s

 

[Nathanael]

(1.8 kg)( 7.5 m/s) / (55kg)
.25 m/s

Yes correct.

Can you do something similar for the other person?

 

[Mltn12]

Yes correct.

Can you do something similar for the other person?

MbVb+MballVball=0
(1.8kg)(7.5m/s) / 75
=.18

 

[Nathanael]

MbVb+MballVball=0
(1.8kg)(7.5m/s) / 75
=.18

Yes, that is right.

The reason is that the person slows down the momentum of the ball (by 1.8 kg times 7.5 m/s) and so the persons momentum must increase by the same amount

 

[Mltn12]

So the final velocity for the girl would be .25m/s while the boys would .18 m/s?

 

[Nathanael]

So the final velocity for the girl would be .25m/s while the boys would .18 m/s?

Yep!

 

[Mltn12]

Wow really? It was that simple? I thought there was more to that problem! Thank you so much!

 

[Nathanael]

No problem!

Conservation of momentum is a very useful tool