A 300kg motorboat is turned off as it approaches a dock and it coasts in toward the dock at .5 m/s. Isaac, whose mass is 62kg, jumps off the front of the boat with a speed of 3m/s relative to the boat. what is the velocity of the boat after Isaac jumps?
To find the velocity of the boat after Isaac jumps off, we need to apply the law of conservation of momentum. According to this law, the total momentum before Isaac jumps off must be equal to the total momentum after Isaac jumps off.
The momentum of an object is calculated by multiplying its mass with its velocity. Therefore, we can calculate the initial momentum of the boat and Isaac, as well as the final momentum of the boat.
Initial momentum (before Isaac jumps off):
Momentum of boat = mass of boat * velocity of boat = 300 kg * 0.5 m/s = 150 kg·m/s
Momentum of Isaac = mass of Isaac * velocity of Isaac = 62 kg * 3 m/s = 186 kg·m/s
Since the boat and Isaac are initially at rest with respect to each other, the total initial momentum is the sum of their individual momenta:
Total initial momentum = Momentum of boat + Momentum of Isaac
= 150 kg·m/s + 186 kg·m/s
= 336 kg·m/s
Now, since the boat and Isaac are separate after Isaac jumps off, the final momentum of the boat must be equal to the negative of Isaac's momentum (due to the law of conservation of momentum).
Final momentum (after Isaac jumps off):
Momentum of boat = -Momentum of Isaac = -186 kg·m/s
Finally, we can find the velocity of the boat after Isaac jumps off using its final momentum and mass:
Final velocity of boat = Final momentum of boat / mass of boat
= (-186 kg·m/s) / 300 kg
= -0.62 m/s
Therefore, the velocity of the boat after Isaac jumps off is -0.62 m/s. The negative sign indicates that the boat is moving in the opposite direction of its initial motion.