Solving a Hockey Puck Collision: Final Velocity

[Veronica_Oles]

Homework Statement

A hockey puck of mass 0.16kg has initial velocity of 2.0m/s[E] and collides with another puck that is initially at rest, has mass of 0.17kg. Once they collide the first puck travels 1.5m/s[N 31 E]. Find final velocity of second puck.

Homework Equations

The Attempt at a Solution

I keep getting an answer that does not match with solutions.

So I first drew it out then made a triangle that does is not a right angle, so I decided to use cosine law.
I am aware that my total momentum is 0.32 kg m/s because P_T=P_T' ...

P_T= (0.16)(2)
=0.32 kg m/s

I also figured out my P₁

P₁= (0.16)(1.5)
= 0.24 kg m/s

I set my triangle up to have a 59° because 90°-31°.

Now I use cosine law to find opposite side of my 59°.

a=√(0.32)²+(0.24)²-2(0.24)(0.32)cos59
P₂= 0.2844 kg m/s

Now I plug this into P=mv

V = 0.2844/0.17
V = 1.7m/s [E 46 S]

Did I do something wrong??

 

[TomHart]

I worked this problem pretty quickly so like all of my solutions, I don't have a lot of confidence in it. But I got the same answer as you did. Maybe we both did it wrong the same way, or possibly the solution is wrong. Hopefully someone else will chime in.

Edit: I just worked the problem a second time and got the same result.

 

[haruspex]

I get the same. Do you know what the answer is supposed to be?

 

[Veronica_Oles]

I get the same. Do you know what the answer is supposed to be?

1.8 m/s. Which is close but usually the answer I get is the exact same as solutions.

 

[haruspex]

1.8 m/s. Which is close but usually the answer I get is the exact same as solutions.

I got 1.67, so 1.8 definitely seems wrong. Equal masses gives 1.77.
I tried swapping the masses but it made the answer 1.88.
I varied the angle from 31 degrees. Had to take it down to about 25 to get 1.8m/s. (The second puck's angle was then 45 degrees S of E.)

 

[TomHart]

@haruspex, I think you're right that they probably solved it using the same mass for both pucks.