Question

A 45.0-kg girl is standing on a 130-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.59 m/s to the right relative to the plank. (Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.)

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

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

Answer 1

here,

mass of girl , m1 = 45 kg

mass of plant , m2 = 130 kg

velocity of girl relative to the plank , v1 = 1.59 m/s

let the velocity of girl and plank relative to ice be v2 and v3

relative velocity , v1 = v2 - v3

1.59 = v2 - v3 .....(1)

and

using conservation of momentum

0 = m1 * v2 + m2 * v3

0 = 45 * v2 + 130 * v3 ....(2)

from (1) and (2)

v2 = 1.18 m/s

v1 = - 0.41 m/s

(a)

the velocity relative to the surface of ice is 1.18 m/s

(b)

the velocity of the plank relative to the surface of ice is - 0.41 m/s