Finding the velocity and angle after an elastic collision

[Northbysouth]

Homework Statement

Jerry and Mary, a young penguin couple, got separated because of an arctic storm. The storm is over and they start looking for each other. Jerry sees Mary first and he starts running on his little legs towards her. Then Mary sees Jerry and starts running as fast as she can toward him. There is ice all over so they end up sliding towards each other. Their precise directions are shown at the figure. When they meet they hug each other so tight that they keep sliding TOGETHER in a new direction, (COUNTERCLOCKWISE from the EAST), with a new speed, . What is and of the young penguin couple?



P^ix = initial momentum of the system in the x direction
p_iy = initial momentum of the system in the y direction
m_j = mass of Jerry
m_m = mass of Mary
P^fx = final momentum of the system in the x direction
p_fy = final momentum of the system in the y direction
v_f = final velocity of the system
θ_f = final angle of the system
v_j = velocity of Jerry
v_m = velocity of Mary

Data:

ψ_j = 15°
ψ = 10°

m_j = 5kg
m_m = 3kg

v_j = 1.2 m/s
v_m = 0.5 m/s

Answer choices:
A) =0.6m/s,θ_f = 287 CCW from the East.
B) =1.1m/s, θ_f= 287 CCW from the East.
C) =0.6m/s,θ_f = 163 CCW from the East.
D) =1.1m/s,θ_f = 163 CCW from the East.
E) =0.6m/s,θ_f = 253 CCW from the East.
F) =1.1m/s,θ_f = 253 CCW from the East

Homework Equations

P =mv

Conservation of momentum

The Attempt at a Solution

P^ix in the x-direction= 5*1.2*sin(15) -2*0.5*sin(10)
= 1.29244 kgm/s

p_iy = 5*1.2*cos(15) - 3*0.5*cos(10)
= 4.31834 kgm/s

Initial velocity of the system = 5.61078 kgm/s

Initial momentum = final momentum

5.16 kgm/s = (5kg+3kg)V_f

V_f = 0.7 m/s

Did I make a mistake in my calculations? Is the 0.1 discrepancy due to a rounding difference?

Then for the final angle:
θ_f = arctan(4.31/1.29)
= 73°

Do I assume that the angle starts from the positive x-axis and moves clockwise? So I would get:
360° - 73° = 287°

 

[CWatters]

I haven't checked all your working but shouldn't that be 3*0.5*sin(10) in...

Pix in the x-direction= 5*1.2*sin(15) -2*0.5*sin(10)

EDIT. Ah it looks like you used 3 to get 1.29244 so that's not the problem.

 

[CWatters]

Are you summing the vectors Pix and Piy correctly? (That's a hint not a question)

 

[Northbysouth]

I thought I had summed them correctly. I can see that I made a typo with
5.16 kgm/s = (5kg+3kg)Vf

which should be

5.61 kgm/s = (5kg+3kg)Vf

But the answer is still 0.7.

 

[CWatters]

When you sum two vectors at right angles it's not

P_ix+P_iy

its

SQRT(P_ix² + P_iy²)Scroll down..

http://www.physicsclassroom.com/class/vectors/u3l1b.cfm