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…

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 of the system $p_i=p_{i - boy}+p_{i - boat}=75\ kg\cdot m/s$.

Step2: Calculate the final - momentum of the combined system

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

Step3: Equate initial and final momenta

According to the law of conservation of momentum $p_i = p_f$. So $75=(50 + 125)v_f$. Solving for $v_f$, we get $v_f=\frac{75}{175}\approx0.43\ m/s$. Since the initial momentum of the boy was forward, the direction of the final velocity is forward.

Answer:

0.43 m/s, forward