Question

a 50 kg boy runs and jumps with a forward velocity of 1.5 m/s into a 125 kg stationary boat. what is the final velocity of the boy/boat system? 0.43 m/s, forward 0.43 m/s, backward 1.1 m/s, forward 1.1 m/s, backward

Explanation:

Step1: Apply conservation of momentum

The initial momentum of the system is just the momentum of the boy since the boat is stationary. The formula for momentum is $p = mv$. The initial momentum of the boy $p_{i - boy}=m_{boy}v_{boy}$, where $m_{boy}=50\ kg$ and $v_{boy}=1.5\ m/s$. So $p_{i - boy}=50\times1.5 = 75\ kg\cdot m/s$. The initial momentum of the boat $p_{i - boat}=m_{boat}v_{boat}=125\times0 = 0\ kg\cdot m/s$. The total initial momentum $p_i=p_{i - boy}+p_{i - boat}=75\ kg\cdot m/s$.

Step2: Calculate final - momentum

After the boy jumps into the boat, they move as one system with mass $m_{total}=m_{boy}+m_{boat}=50 + 125=175\ kg$. Let the final velocity of the system be $v_f$. The final momentum $p_f=m_{total}v_f$.

Step3: Equate initial and final momenta

According to the law of conservation of momentum $p_i = p_f$. So $75\ kg\cdot m/s=175\ kg\times v_f$. Solving for $v_f$, we get $v_f=\frac{75}{175}\approx0.43\ m/s$. The positive sign indicates the direction is forward.

Answer:

0.43 m/s, forward