Batman (mass = 89.1 kg) jumps straight down from a bridge into a boat (mass = 452 kg) in which a criminal is fleeing. The velocity of the boat is initially +12.9 m/s. What is the velocity of the boat after Batman lands in it?
To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
The momentum of an object is calculated by multiplying its mass by its velocity.
Given:
Mass of Batman (m1) = 89.1 kg
Mass of boat (m2) = 452 kg
Initial velocity of the boat (v1) = +12.9 m/s
Let's assume the final velocity of the boat after Batman lands in it is v2.
Using the principle of conservation of momentum, we can write the equation:
(mass of Batman × velocity of Batman) + (mass of boat × initial velocity of boat) = (mass of Batman + mass of boat) × final velocity of boat
(89.1 kg × 0 m/s) + (452 kg × 12.9 m/s) = (89.1 kg + 452 kg) × v2
(0 kg⋅m/s) + (5828.8 kg⋅m/s) = (541.1 kg) × v2
5828.8 kg⋅m/s = 541.1 kg × v2
Now we can solve for the final velocity of the boat (v2):
v2 = (5828.8 kg⋅m/s) / (541.1 kg)
v2 ≈ 10.77 m/s
Therefore, the velocity of the boat after Batman lands in it is approximately 10.77 m/s.
To solve this problem, we need to apply the law of conservation of momentum. According to this law, the total momentum before Batman jumps into the boat should be equal to the total momentum after he lands in it.
Momentum is defined as the product of mass and velocity. Therefore, we need to calculate the initial momentum of Batman and the boat separately and then calculate the final momentum.
1. Calculate the initial momentum of Batman and the boat separately:
Initial momentum of Batman = mass of Batman x velocity of Batman
= 89.1 kg x 0 m/s (as Batman is initially at rest)
= 0 kg·m/s
Initial momentum of the boat = mass of the boat x velocity of the boat
= 452 kg x 12.9 m/s
= 5828.8 kg·m/s
2. Calculate the final momentum by considering Batman and the boat together:
Final momentum = (mass of Batman + mass of the boat) x velocity of the boat after Batman lands
= (89.1 kg + 452 kg) x v
= 541.1 kg x v
Since the total momentum before and after Batman lands in the boat should be the same, we can equate the two equations:
Initial momentum = Final momentum
0 kg·m/s = 541.1 kg x v
To find the velocity of the boat after Batman lands (v), we can rearrange the equation:
v = 0 kg·m/s / 541.1 kg
v ≈ 0 m/s
Therefore, the velocity of the boat after Batman lands in it is approximately 0 m/s. This means the boat comes to a stop upon Batman's jumps.