Question

A boy and a cart are moving in the same direction with the boy going twice as fast as the cart .When he gets into the cart ,the speed of the cart increases by20% .. Find the ratio of mass of cart to mass of boy

Answer 1

The ratio of the mass of cart and mass of boy will be 4:1

Explanation :

Conservation of momentum will be applied here,

Let the mass of the boy = x

let the mass of the cart = y

Let the speed of the cart be 100 m/s before

=> speed of the boy = 200 m/s

Hence momentum of the system before the boy gets into cart;

= 200x + 100y..............eq1

After the boy gets into the cart, effective mass = x + y

speed of the cart = 100 + 20% = 120 m/s

Hence net momentum of the system

= 120(x + y)

= 120 x + 120 y.....................eq2

since total momentum of the system will be conserved, hence equating eq1 and eq2 we get

200x + 100y = 120x + 120y

=> 80x = 20y

=> y/x = 80/20 = 4

Hence the ratio of the mass of cart and mass of boy will be 4:1