Solving Boy & Girl's Velocity After Snow Ball Toss

[simpreza2]

Im having trouble with this problem...

A 35kg girl is standing near and to the left of a 43kg boy on a frictionless surface of a frozen pond. The boy tosses a .75kg snow ball to the girl with a horizontal speed of 6.2m/s. What are the velocities of the boy and girl immediately after the girl catches the snow ball?

I don't really know where to start but I found a similar problem in my notes and it looks like this...

An astronaut(90kg) throws a wrench(5kg). Find the final velocity of antronaut. And we used this equation...
$$P_{final}=m_{astro}v_{final astro} + m_{wrench}v_{final wrench}$$

I am thinking I need to split the problem into two pieces. The ball leaving the boys hand and then the girl catching the ball. Would I use the same formula as above for this problem like so...

$$P_{final}=m_{boy}v_{final boy} + m_{snow ball}v_{final snow ball}$$

$$P_{final}=m_{girl}v_{final girl} + m_{snow ball}v_{final snow ball}$$

 

[dextercioby]

Im having trouble with this problem...

A 35kg girl is standing near and to the left of a 43kg boy on a frictionless surface of a frozen pond. The boy tosses a .75kg snow ball to the girl with a horizontal speed of 6.2m/s. What are the velocities of the boy and girl immediately after the girl catches the snow ball?

I don't really know where to start but I found a similar problem in my notes and it looks like this...

An astronaut(90kg) throws a wrench(5kg). Find the final velocity of antronaut. And we used this equation...
$$P_{final}=m_{astro}v_{final astro} + m_{wrench}v_{final wrench}$$

I am thinking I need to split the problem into two pieces. The ball leaving the boys hand and then the girl catching the ball. Would I use the same formula as above for this problem like so...

$$P_{final}=m_{boy}v_{final boy} + m_{snow ball}v_{final snow ball}$$

$$P_{final}=m_{girl}v_{final girl} + m_{snow ball}v_{final snow ball}$$

That's a good idea,but remember that the notations u made can be misleading.I mean the notations for the quantities related to the snowball.In your formulas,the final velocities for the snowball are different.For the boy,it's 6.2 m/s,but in the case of the girl,it will be the same with the girl's and that's something u'll have to figure out yourself.

PS.Does the girl get the snowball in the face?

 

[simpreza2]

In your formulas,the final velocities for the snowball are different.For the boy,it's 6.2 m/s,but in the case of the girl,it will be the same with the girl's and that's something u'll have to figure out yourself.

I don't understand this part..."but in the case of the girl,it will be the same with the girl's" Maybe I am reading it wrong but I just don't get it right now. If you could re-phrase it that would be aweosme. Thanks

 

[dextercioby]

I don't understand this part..."but in the case of the girl,it will be the same with the girl's" Maybe I am reading it wrong but I just don't get it right now. If you could re-phrase it that would be aweosme. Thanks

I spelled it wrong,just the way u did with "awesome" .I was tryin to say:"the final speed of the snowball is a relative concept,meaning that in the subsystem formed by the boy & the snowball,it has the value of 6.2 m/s,while in the subsystem formed by the girl & the snowball,it has an unknown value,equal to the final speed of the girl,as,apparently "she gets it".
From solving the 2 equations,u'll find the three final velocities (2 of them equal) about which the problem is asking u.

Daniel.

 

[simpreza2]

I was tryin to say:"the final speed of the snowball is a relative concept,meaning that in the subsystem formed by the boy & the snowball,it has the value of 6.2 m/s,while in the subsystem formed by the girl & the snowball,it has an unknown value,equal to the final speed of the girl,as,apparently "she gets it".
From solving the 2 equations,u'll find the three final velocities (2 of them equal) about which the problem is asking u.

Daniel.

I think I get what your saying. Subsystem1 with the boy, v snowball is 6.2 m/s but by the time it reaches the girl in subsystem2 it has a different velocity, one equal to the final velocty of the girl.

I just realized how do I solve the $$P_{final}=m_{boy}v_{final boy} + m_{snow ball}v_{final snow ball}$$ when I have 2 variables? I don't know the Pfinal or the v final boy?

 

[simpreza2]

I tried to look at it again and I still can't figure it out. Any one got any tips...

 

[matt.o]

you are correct, the problem can be separated into 2 systems.

use the fact that the momentum before must equal the momentum after. ie.

$$P_{boy,snowball,initial}=0=P_{boy,after}+P_{snowball}$$

you can now solve for the boys velocity, as you know the masses and the snowball's velocity. You can use the same principle for the girl's final velocity. ie you know the initial momentum of the girl and snowball. use this to solve for the combined final velocity of the snowball+girl (assuming the girl caught it!)