A 71 kg skater and a 59 kg skater stand at rest on frictionless ice. They push off, and the 71 kg skater moves at 2.5 m/s in the + x-direction.
What's the other's velocity?
momentum is conserved
71 * 2.5 = 59 * v
the direction is negative x
To find the velocity of the other skater, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the skaters push off is equal to the total momentum after they push off. In other words, the initial momentum of the system is equal to the final momentum.
The momentum of a skater can be calculated by multiplying its mass by its velocity. Let's assume the velocity of the other skater is v.
Before the push-off:
The momentum of the 71 kg skater = (Mass of 71 kg skater) × (Velocity of 71 kg skater)
The momentum of the other skater = (Mass of other skater) × (Velocity of other skater)
After the push-off:
The momentum of the 71 kg skater = (Mass of 71 kg skater) × (Final velocity of 71 kg skater)
The momentum of the other skater = (Mass of other skater) × (Final velocity of other skater)
Given:
Mass of 71 kg skater = 71 kg
Velocity of 71 kg skater = 2.5 m/s
To find the velocity of the other skater, we can set up the conservation of momentum equation:
(71 kg) × (2.5 m/s) + (59 kg) × (0 m/s) = (71 kg) × (Final velocity of 71 kg skater) + (59 kg) × (Final velocity of other skater)
Simplifying the equation:
177.5 kg·m/s = (71 kg) × (Final velocity of 71 kg skater) + (59 kg) × (Final velocity of other skater)
Since the initial velocity of the other skater is 0 m/s, we know that the initial momentum of the other skater is 0. This means we can simplify the equation further:
177.5 kg·m/s = (71 kg) × (Final velocity of 71 kg skater) + 0
Now we can solve for the final velocity of the other skater:
Final velocity of other skater = (177.5 kg·m/s) / (59 kg)
Calculating this:
Final velocity of other skater = 3 m/s
Therefore, the velocity of the other skater is 3 m/s in the positive x-direction.