How can I solve this?

Question

A 44.4-kg girl is standing on a 161-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.60î m/s relative to the plank.

(a) What is the velocity of the plank relative to the ice surface?

_____ î m/s

(b) What is the girl's velocity relative to the ice surface?

_____ î m/s

Answer 1

Given:

Let

M1 = 44.4 kg (girl)

M2 = 161 kg (plank)

V1o = 0 m/s (initial velocity of the girl is zero)

V2o = 0 m/s (initial velocity of the plank is zero)

V1' = 1.60 m/s

Solution

Apply Conservation of momentum

m1V1o + m2V2o = M1V1'+M2V2'

0 = M1V1'+M2V2'

V2' = -M1V1'/M2 = -0.441 m/s

Need to apply relative velocity equations

a)

Let 1 be the girl, 2 be the plank and 3 be the surface of ice

Absolute velocity of surface of ice is zero... V3 = 0

V1 = V3 + V_1/3

V3 = 0

V1 = 1.60 m/s

b)

V2 = V3 + V_2/3

V3 = 0

V2 = -0.441 m/s