There are two set pieces in a theater sitting on platforms with wheels. One is a tree with a mass of 50 kg. It is moving at 3 m/s. The other is a fence with a mass of 30 kg. If the two set pieces have equal momentum, how fast is the fence moving?
A. 3 m/s B. 5 m/s
C. 30 m/s D. 90 m/s
To solve this problem, we need to 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 there is no external force acting on the system.
In this case, the momentum of an object is calculated by multiplying its mass (m) by its velocity (v). So, let's calculate the momentum of each set piece:
Momentum of the tree = mass of the tree × velocity of the tree
= 50 kg × 3 m/s
= 150 kg·m/s
Since the two set pieces have equal momentum, the total momentum of the system is 150 kg·m/s. Now we need to find the velocity of the fence.
Momentum of the fence = mass of the fence × velocity of the fence
= 30 kg × velocity of the fence
Since the momentum of the fence is equal to 150 kg·m/s, we can set up an equation:
30 kg × velocity of the fence = 150 kg·m/s
Now we can solve for the velocity of the fence:
velocity of the fence = 150 kg·m/s / 30 kg
= 5 m/s
Therefore, the correct answer is B. 5 m/s.