a man steps out of a rowboat into a dock. The man has a mass of 80 kg and moves forward with a velocity of 1.5 m/s. If the boat has a mass of 120 kg. and was initially at rest, what is its final velocity?
initial momentum = 0 so final momentum = 0
0 = 80*1.5 + 120 * V
V = - 120/120 = -1 meter/second
To find the final velocity of the rowboat, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event should be equal to the total momentum after the event.
The initial momentum of the system (man + boat) is zero, since the boat is initially at rest. The final momentum of the system should also be zero, as no external forces act on the system.
The momentum of an object can be calculated using the formula: momentum = mass * velocity.
Let's denote the final velocity of the boat as "v_b" and the final velocity of the man as "v_m".
The initial momentum of the system is:
Initial momentum = (mass of man * velocity of man) + (mass of boat * velocity of boat)
Since the boat is initially at rest, we can rewrite the equation as:
0 = (80 kg * 1.5 m/s) + (120 kg * 0)
Simplifying the equation:
0 = 120 kg * 1.5 m/s
Now, let's solve for the final velocity of the boat:
mass of boat * velocity of boat = - (mass of man * velocity of man)
(120 kg * v_b) = - (80 kg * 1.5 m/s)
Cross multiplying and rearranging the equation:
120 kg * v_b = - (80 kg * 1.5 m/s)
120 kg * v_b = - 120 kg * 0.375 m/s
Dividing both sides of the equation by 120 kg:
v_b = - 0.375 m/s
Therefore, the final velocity of the boat, after the man steps out, is -0.375 m/s. The negative sign indicates that the boat moves in the opposite direction to the man's movement.