Calculating Velocity of Ice Skater After Throwing Snowball

[PierceJ]

Homework Statement

A 63 kg ice skater, at rest on frictionless ice, tosses a 4.06 kg snowball with velocity given by v = ( -14.3 i + 17.2 j ) m/s, where the x and y axes are both in the horizontal plane. Find the subsequent velocity of the skater.

Homework Equations

p = mv
p = m₁v₁+...

The Attempt at a Solution

I started by finding the total momentum of the system by multiplying 4.06 by each part of the vector and I got:
( -58.058i + 69.832j )
Then I set that equal to the two masses added together times v.
( -58.058i + 69.832j ) = 67.06v
v = ( -0.8658i + 1.041j)

 

[DrClaude]

What is your question? Where are the units? What about significant digits?

 

[PierceJ]

The question is there "Find the subsequent velocity of the skater."
The units are also there, m/s
4 significant digits

 

[PeroK]

Homework Statement

A 63 kg ice skater, at rest on frictionless ice, tosses a 4.06 kg snowball with velocity given by v = ( -14.3 i + 17.2 j ) m/s, where the x and y axes are both in the horizontal plane. Find the subsequent velocity of the skater.

Homework Equations

p = mv
p = m₁v₁+...

The Attempt at a Solution

I started by finding the total momentum of the system by multiplying 4.06 by each part of the vector and I got:
( -58.058i + 69.832j )
Then I set that equal to the two masses added together times v.
( -58.058i + 69.832j ) = 67.06v
v = ( -0.8658i + 1.041j)

Is the skater moving in the same direction as the ball he has just thrown?

Or was the ball thrown at him, as the title of your post suggests?

 

[haruspex]

If the skater moves off with velocity w,and the masses are m (snowball) and M, what is the conservation equation (in symbols, not numbers)?

 

[PierceJ]

p = Mw + mv?

 

[DrClaude]

The question is there "Find the subsequent velocity of the skater."

I meant what is your question, why did you post? I now realize that I misread the question, as I had in mind what you wrote for the title of the thread. But is the problem really "Ball thrown at skater," as PeroK also asked?

The units are also there, m/s

I meant in your answer.

QUOTE="PierceJ, post: 5030654, member: 546115"]
4 significant digits[/QUOTE]
Why 4? Is this compatible with the data from the problem?

But you should start by answering haruspex's question correctly.

 

[PierceJ]

I realize now that I have read the problem wrong, but even so I still don't know how to answer haruspex's question. I know this forum is designed for me to figure out with only a little help but I'm completely lost here.

 

[DrClaude]

I realize now that I have read the problem wrong, but even so I still don't know how to answer haruspex's question. I know this forum is designed for me to figure out with only a little help but I'm completely lost here.

The question is about conservation. What can you write that relates before the throw to after the throw?

 

[PierceJ]

(m₁+m₂)( -14.3 i + 17.2 j ) = m₁v₁+m₂v₂?

 

[DrClaude]

Start from the momentum.

 

[haruspex]

(m₁+m₂)( -14.3 i + 17.2 j ) = m₁v₁+m₂v₂?

It says the skater throws, not catches, the snowball. What is the momentum of the system before the skater does so? What is the momentum of the snowball after the skater has thrown it?

 

[PierceJ]

The momentum before is 0? Cause the guy isn't moving?
Momentum of the snowball after is its mass times the velocity given in the problem.

 

[haruspex]

The momentum before is 0? Cause the guy isn't moving?
Momentum of the snowball after is its mass times the velocity given in the problem.

Right. So have another go at the equation.

 

[PierceJ]

Ah I see, I got it now. Thank you for putting up with me haha.