Batman (mass = 75.6 kg) jumps straight down from a bridge into a boat (mass = 631 kg) in which a criminal is fleeing. The velocity of the boat is initially +10.4 m/s. What is the velocity of the boat after Batman lands in it?
To get started you need to use the principle conservation of linear momentum equation:
(mass1)*(finalvelocity1)+(mass2)*(finalvelocity2)= (mass1)*(intialvelocity1)+ (mass2)*(initialvelocity2)
This problem only cares about the horizontal motion, so don't think about how Batman's vertical fall effects the boat. Since he is falling straight down he has no vertical velocity. The final velocity for Batman will be the same as for the boat.
mass1 = batman = 75.6 kg
mass2 = boat = 631 kg
initial velocity 1 = batman's initial velocity = 0 m/s
initial velocity 2 = boat's initial velocity = 10.4 m/s
finalvelocity1 = finalvelocity2
so you simply plug in the numbers and solve for their final velocity
To solve this problem, we can make use of the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces act on it.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, we need to calculate the initial momentum of the boat and Batman separately and then find their combined momentum.
1. Calculate the initial momentum of the boat:
Momentum of the boat = mass of the boat × velocity of the boat
Mass of the boat = 631 kg
Velocity of the boat = +10.4 m/s (since it is initially moving in the positive direction)
Initial momentum of the boat = 631 kg × 10.4 m/s
2. Calculate the momentum of Batman:
Mass of Batman = 75.6 kg
Batman is initially at rest, so his initial velocity is 0 m/s.
Initial momentum of Batman = mass of Batman × initial velocity of Batman
Since no external forces act on the system, the total momentum before and after Batman lands in the boat must be the same. Therefore, we can use this principle to find the velocity of the boat after Batman lands.
3. Calculate the combined momentum after Batman lands:
Combined momentum = momentum of the boat + momentum of Batman
Since momentum is a vector quantity, we need to consider its direction as well. In this case, the direction can be taken as positive (since Batman jumps straight down).
4. Calculate the velocity of the boat after Batman lands:
We divide the combined momentum by the total mass of the system (the boat and Batman) to get the velocity.
Velocity of the boat after Batman lands = Combined momentum / (mass of the boat + mass of Batman)
By following these calculations, you can find the velocity of the boat after Batman lands in it.