(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

P =mv

Conservation of momentum

3. 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°

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# Homework Help: Finding the velocity and angle after an elastic collision

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