Two ice skaters are initially at rest. The 78.2 kg male ice skater pushes his 48.5 kg female partner forward and away from his body with a velocity of 8.46m/sec. What is the male skater's velocity as a result of the push?
conserve momentum
78.2v + 48.5*8.46 = 0
To solve this problem, we will apply the principle of conservation of momentum. According to this principle, the total momentum before the push should be equal to the total momentum after the push.
The momentum of an object is defined as the product of its mass and velocity:
Momentum = mass × velocity
Before the push, both ice skaters are at rest, so their initial velocities are zero. Therefore, the initial total momentum is zero.
Initial total momentum = m1 × v1 + m2 × v2
= 78.2 kg × 0 m/s + 48.5 kg × 0 m/s
= 0 kg·m/s
After the push, the male skater (skater 1) has a velocity of 8.46 m/s, and the female skater (skater 2) moves in the opposite direction with the same speed.
Let's call the resulting velocity of the male skater v1 and the resulting velocity of the female skater v2.
So, the final total momentum is:
Final total momentum = m1 × v1 + m2 × v2
Since the total momentum is conserved, we have:
Initial total momentum = Final total momentum
0 kg·m/s = 78.2 kg × v1 + 48.5 kg × (-8.46 m/s)
Now we can solve for v1, the velocity of the male skater:
0 = 78.2 kg × v1 - 48.5 kg × 8.46 m/s
Rearranging the equation:
v1 = (48.5 kg × 8.46 m/s) / 78.2 kg
Now we can calculate v1:
v1 = (410.61 kg·m/s) / 78.2 kg
≈ 5.25 m/s
Therefore, the male skater's velocity as a result of the push is approximately 5.25 m/s.