Impulse and momentum in two dimensions - velocity question

[Specter]

Homework Statement

Sorry for another question so soon, I am not sure if there is a limit on how many I can ask. I try to keep it to a minimum but sometimes I can't figure it out on my own.

Question:

In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with 0.40 kg puck b, which is initially at rest. Puck A moves off at 4.2 m/s [W 30° N]. Find the final velocity of puck B

Homework Equations

P_To=P_TF
Pythagorean theorem

The Attempt at a Solution

I just want to make sure all of my steps are correct. I did see some other people get different answers such as 1.9 m/s [W 58 N], and another person got the same direction as me but the velocity was 6.3 m/s.

Could my answers be off due to rounding?

Let north and east be positive:

Use conservation of momentum for the components:

x components:
P_TOx = P_TFx
m₁v_1ox+m₂v_2ox=m₁v_1fx+m₂v_2fx
(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx
v_2fx = -0.8 m/s.

y components:
P_TOy = P_TFy
m₁v_1oy+m₂v_2oy=m₁v_1fy+m₂v_2fy
(0.30)(0)+(0.40)(0) = (0.30)(2.1)+(0.40)v_2fy
v_2fy = -1.03 m/s

Now I have:
v_2f = ??
v_2fx = -0.8 m/s
v_2fy = -1.03 m/s

Pythagorean theorem to find the final velocity:
v_2f = √1.03²+0.8²
v_2f = 1.3 m/s

To find direction:

θ=tan^-1(1.03/0.8)
θ=52.16°

The final velocity of puck B is 1.3 m/s [W 52° S]

 

[TSny]

x components:
(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx

Looks good.

v_2fx = -0.8 m/s.

Check this.

y components:
(0.30)(0)+(0.40)(0) = (0.30)(2.1)+(0.40)v_2fy

Looks good.

v_2fy = -1.03 m/s

Check this.

The rest of your work looks good in terms of method.

 

[Specter]

Looks good.
Check this.

Looks good.
Check this.

The rest of your work looks good in terms of method.

I'm not sure what I did wrong there. I did the calculations again and still got the same answers :(

 

[TSny]

I'm not sure what I did wrong there. I did the calculations again and still got the same answers :(

Can you show the steps in going from
(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx
to v_2fx = -0.8 m/s?

I think you might be making a mistake in how you are treating the (0.40) in the expression (0.40)v_2fx

 

[Specter]

Can you show the steps in going from
(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx
to v_2fx = -0.8 m/s?

I think you might be making a mistake in how you are treating the (0.40) in the expression (0.40)v_2fx

This is my new answer:

(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx
1.5 = (-0.692) v_2fx
1.5 + 0.692 = v_2fx
2.192 = v_2fx

The way I did it in my original post was

v_2fx= -1.5 -(-0.0692)
= -0.8


for the y component
(0.30)(0)+(0.40)(0)=(0.30)(2.1)+(0.40)v_2fy
0 = 1.03 _v2fy
1.03 = v_2fy

 

[TSny]

This is my new answer:

(0.30)(-5.0)+(0.40)(0) = (0.30)(-3.64)+(0.40)v_2fx
1.5 = (-0.692) v_2fx

On the left side you are multiplying a positive number with a negative number. What should be the sign of the left side?

I don't follow how you simplified the right side to (-0.692) v_2fx. Can you show more steps? Note that the 0.40 on the right is multiplying v_2fx.

 

[Specter]

Ignore this post. I forgot to quote you in the reply.

 

[Specter]

On the left side you are multiplying a positive number with a negative number. What should be the sign of the left side?

I don't follow how you simplified the right side to (-0.692) v_2fx. Can you show more steps? Note that the 0.40 on the right is multiplying v_2fx.

This is how I got -0.692.

(0.30)(-5.0)+(0.40)(0)=(0.30)(-3.64)+(0.40)v_2fx
-1.5 + 0 = -1.092 + (0.40) v_2fx
-1.5 = -0.692 (v_2fx)

 

[TSny]

This is how I got -0.692.

(0.30)(-5.0)+(0.40)(0)=(0.30)(-3.64)+(0.40)v_2fx
-1.5 + 0 = -1.092 + (0.40) v_2fx

OK

-1.5 = -0.692 (v_2fx)

Quick review: Which of the following expressions equals 7x? (Or do they both equal 7x?)

2 + 5x

2x + 5x

 

[Specter]

OK

Quick review: Which of the following expressions equals 7x? (Or do they both equal 7x?)

2 + 5x

2x + 5x

I haven't been in a math class for 2 and a bit years now. I should probably know most of this stuff, and I don't.

But..

2x + 5x = 7x

 

[haruspex]

I haven't been in a math class for 2 and a bit years now. I should probably know most of this stuff, and I don't.

But..

2x + 5x = 7x

So have another go at your last step in post #8.

 

[Specter]

So have another go at your last step in post #8.

-1.5 = (-0.692) v_2fx

Maybe I can divide each side to solve for v?

-1.5/-0.692 = -0.692/-0.692
v_2fx = 2.16

 

[haruspex]

-1.5 = (-0.692) v_2fx

No, that's already wrong. Go back to the line before that in post #8.

 

[Specter]

No, that's already wrong. Go back to the line before that in post #8.

(0.30)(-5.0) + (0.40)(0) = (0.30)(-3.64) + (0.40) v_2fx
-1.5 + 0 = -1.092 + (0.40) v_2fx
-0.408 = (0.40)v_2fx
-1.02 = v_2fx

 

[haruspex]

(0.30)(-5.0) + (0.40)(0) = (0.30)(-3.64) + (0.40) v_2fx
-1.5 + 0 = -1.092 + (0.40) v_2fx
-0.408 = (0.40)v_2fx
-1.02 = v_2fx

Much better.

 

[Specter]

Much better.

Thanks for the help. It was a stupid mistake!