Answer to Question #165282 in Atomic and Nuclear Physics for Katrina Robles

Question

After sledging down a hill onto a frozen lake, a boy and a girl are sitting at rest. The combined mass of the kids and the sled is 210 kg. The 70 kg boy jumps north at 6.5 m/s and the 50 kg girl jumps to the south at 8.1 m/s.

How fast and in what direction will the sled be traveling?

Answer 1

The mass of a sledge is $210-70-50 = 90$ kg.

We may use the conservation of the linear momentum law. At the initial moment the total momentum is 0 because the system is in rest.

Let the x-axis be directed from the initial point to the north. When kids jump, their linear momentum becomes $m_b v_b - m_gv_g + m_sv_s$ and this sum of momenta should also be 0.

Therefore,

$m_sv_s = m_gv_g - m_bv_b, \;\; v_s = \dfrac{m_gv_g - m_bv_b}{m_s}=\dfrac{50\cdot8.1-70\cdot6.5}{90} = -0.56\,\mathrm{m/s}.$ Therefore, this velocity is directed opposite to the north, namely, to the south.