- #1
Northbysouth
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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?
Pix = initial momentum of the system in the x direction
piy = initial momentum of the system in the y direction
mj = mass of Jerry
mm = mass of Mary
Pfx = final momentum of the system in the x direction
pfy = final momentum of the system in the y direction
vf = final velocity of the system
θf = final angle of the system
vj = velocity of Jerry
vm = velocity of Mary
Data:
ψj = 15°
ψ = 10°
mj = 5kg
mm = 3kg
vj = 1.2 m/s
vm = 0.5 m/s
Answer choices:
A) =0.6m/s,θf = 287 CCW from the East.
B) =1.1m/s, θf= 287 CCW from the East.
C) =0.6m/s,θf = 163 CCW from the East.
D) =1.1m/s,θf = 163 CCW from the East.
E) =0.6m/s,θf = 253 CCW from the East.
F) =1.1m/s,θf = 253 CCW from the East
Homework Equations
P =mv
Conservation of momentum
The Attempt at a Solution
Pix in the x-direction= 5*1.2*sin(15) -2*0.5*sin(10)
= 1.29244 kgm/s
piy = 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)Vf
Vf = 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:
θf = 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°