Answer:
v_g,i = 1.208 m/s
Explanation:
We are given;
Mass of girl; m_g = 47.2 kg
Mass of plank; m_p = 177 kg
Let the velocity of girl to ice be v_g,i
Let the velocity of plank to ice be v_p,i
Since the velocity of the girl is 1.53 m/s relative to the plank, then;
v_g,i + v_p,i = 1.53
From conservation of momentum;
m_g × v_g,i = m_p × v_p,i
Thus;
47.2(v_g,i) = 177(v_p,i)
Dividing both sides by 47.2 gives;
v_g,i = 3.75(v_p,i)
v_pi = (v_g,i)/3.75
Thus, from v_g,i + v_p,i = 1.53, we have;
v_g,i + ((v_g,i)/3.75) = 1.53
v_g,i(1 + 1/3.75) = 1.53
1.267v_g,i = 1.53
v_g,i = 1.53/1.267
v_g,i = 1.208 m/s
