During an ice skating event, two partners (a 60.0 kg boy and a 45.0 kg girl) pus

Question

During an ice skating event, two partners (a 60.0 kg boy and a 45.0 kg girl) pushed
away from each other. Before they came into contact, the girl was moving toward the
boy with a speed of 3.00 m/s. The move was timed perfectly, so that after they pushed
off, they moved in opposite directions, each with the same speed of 3.00 m/s. Before
and after they pushed off, the boy and girl only moved forward or backward along the
same line as the initial velocity of the girl. You should assume that during the time
that the two were in contact, friction was small enough to be ignored.
a) Using only the information you have been provided thus far, ignore all sources of
friction and external forces, and find the velocity of the boy before the two skaters
pushed off of each other.
b) Now you are given the additional piece of information that they pushed off with
their hands for one and a half seconds (1.50 s). You may use this piece of
information for the rest of this question (through part f). Find the average
acceleration of the girl during the time the two were in contact.
c) Ignoring all sources of friction and external forces, find the magnitude of the
average force that the boy exerted on the girl during the time they were in contact.
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d) Ignoring all sources of friction and external forces, find the magnitude of the average force that the girl exerted on the boy during the time they were in contact.
e) Find the average acceleration of the boy during the time the two were in contact.
f) Compare the magnitudes of your previous four answers:
i) How does the magnitude of your answer to part b compare to the magnitude of your answer to part c? If they are the same explain what principle causes them to be the same. If they are different explain what principle causes them to be different.
ii) How does the magnitude of your answer to part a compare to the magnitude of your answer to part d? If they are the same explain what principle causes them to be the same. If they are different explain what principle causes them to be

Explanation / Answer

1) momentum

45*3 + 60*v = 45*-3 + 60*3

v=-1.5 m/s

2)

F = dp/dt

F = m dv/dt

F = ma

so a = dv/dt = (-3 -3)/1.5 = -6/1.5 = -4 m/s^2

3) F = ma = 45*4 = 180 N

4) newtons third law

F girl = F boy

so F = 180 N

5)

a = F/m = 180/60 = 3 m/s^2

6)

a) they are the same since newtons third law

b) different since different masses

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