Mrs. Wade is trying to escape his enemy on a speedboat, but his boat won't start and remains stationary in the water. Her enemy's boat is twice the mass of Mrs. Wade's boat and collides with her boat at 50 m/s. After the collision, the enemy boat is completely stationary. How fast is Mrs. Wade's boat moving?
a
50 m/s
b
25 m/s
c
100 m/s
d
0 m/s
d) 0 m/s
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant before and after a collision.
Let's assume the mass of Mrs. Wade's boat is m, and the mass of the enemy's boat is 2m (twice the mass of Mrs. Wade's boat).
Before the collision:
The momentum of Mrs. Wade's boat = m × velocity of Mrs. Wade's boat
The momentum of the enemy's boat = 2m × velocity of the enemy's boat
Since the enemy's boat collides with Mrs. Wade's boat and is completely stationary after the collision, the momentum of the enemy's boat becomes zero.
After the collision:
The momentum of Mrs. Wade's boat remains the same and is given by m × velocity of Mrs. Wade's boat, which is what we want to find.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
m × velocity of Mrs. Wade's boat + 2m × velocity of the enemy's boat = 0
Substituting the given values:
m × velocity of Mrs. Wade's boat + 2m × 50 m/s = 0
Simplifying the equation:
velocity of Mrs. Wade's boat + 2 × 50 m/s = 0
velocity of Mrs. Wade's boat + 100 m/s = 0
velocity of Mrs. Wade's boat = -100 m/s
Since velocity cannot be negative in this context, the correct answer is 0 m/s (option d).