A 45.2-kg girl is standing on a 151-kg plank. Both originally at rest on a froze

Question

A 45.2-kg girl is standing on a 151-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 1.44i m/s relative to the plank. What is the velocity of the plank relative to the ice surface? Your response differs from the correct answer by more than 10%. Double check your calculations.! m/s What is the girl's velocity relative to the ice surface? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate result: to at least four-digit accuracy to minimize roundoff error. i m/s

Explanation / Answer

Considering girl and plank a system ,the momentum will remain conserve

Conservation of momentum

Momentum of system =momentum of girl +momentum of plank = 0 with respect to surface of frozen lake. since initially momentum is zero
let velocity of plank be v2 m/s with respect to ic surface and velocity of girl be v1 with respect to ice surface

m1v1 + m2v2=0 (i)

given velocity of girl with respect to ice surface=1.44 m/s

v1=1.44+ v2

putting v1=1.44+v2 in (i)

v2=- 0.3317 m/s i ( - means in -x direction)

v1=1.1083 m/s i ( in +x direction)

(a) velocity of plank =v2= 0.33 m/s in opposite direction

(b) velocity of girl with respect to ice surface=v1=1.108 m/s in same direction

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