Question

A 40 kg boy is stationary on a 30 kg plank that is sliding at 5 m/s to the right across a frictionless pond. The boy then turns and starts walking on the plank at arate of 4 m/s to the left, relative to the plank. What is the speed of the plank relative to the pond now ?

Answer 1

lets say Velocity of boy relative to pond be Vb and that of plank relative to pond be Vp.

so after boy starts walking with speed of 4m/s left

assume left is -ve and right +ve

=> -4 = Vb - Vp

=> Vb = Vp -4

velocity of boy relative to pond is Vp - 4

applying conservation of momentum

initial momentum = (40+30)* 5 = 350

final momentum = 40*Vb + 30*Vp

350 = 40*Vb + 30*Vp

350 = 40*(Vp - 4) + 30*(Vp)

350 = 70Vp - 160

510 = 70Vp

Vp = 510/70 = 7.285

velocity of plank relative to pond is 7.285 m/s