Question

A girl of mass 40 kg jumps with a horizontal velocity of 5 m/s onto a stationary cart with frictionless wheels. The mass of the cart is 3 kg. What is her velocity as the cart starts moving? Assume that there is no external unbalanced force working in the horizontal direction.

Answer 1

Given

1. Mass of the girl ($m_g$) = 40 kg.
2. Mass of the cart ($m_c$) = 3 kg.
3. Initial velocity of the cart ($u_c$) = 0 m/s.
4. Initial velocity of the girl ($u_g$) = 5m/s.

Concepts to be used

1. Final velocity of the cart and girl will be the same as the girl jumps over the cart i.e,$v_g=v_c=v.$
2. Conservation of momentum will be used.

Calculation of velocity of the cart

1. Initial momentum = Final momentum.
2. $m_g{u}_g+m_c{u}_c=m_g{v}_g+m_c{v}_c$
3. $40\times 5+3\times 0=(40+3)v$.
4. $200=43v$
5. $v=\frac{200}{43}=4.65m/s.$

Hence, the velocity of the cart is 4.65 m/s.