Question

The mass of the skateboard is 1.8kg and the mass of the skateboarder is 42kg.

Calculate the velocity at which the skateboard moves backwards if the skateboarder jumps forward at a velocity of 0.3m/s.

Please help asap ;-;

Answer 1

Total momentum must be conserved since there are no external forces in the horizontal direction on the skateboarder or the skateboard.

Momentum before the jump:
$P = m_1v_1 + m_2v_2 = (1.8kg)(0) + (42kg)(0) = 0$

Momentum after the jump:
$P = m_1v_1 + m_2v_2 = (1.8kg)(v_1) + (42kg)(0.3 \frac{m}{s} ) = 0$

Solving for the velocity v:
$v_1 = - \frac{m_2v_2}{m_1} = - \frac{(42kg)(0.3 \frac{m}{s} )}{1.8kg} = -7 \frac{m}{s}$