Question

two figure skaters, one weighing 655 n and the other 775 n, push off against each other on very smooth ice. if the heavier skater travels at 1.60 m/s, how fast will the lighter one travel?

Answer 1

The lighter skater will travel at a speed of 1.89 m/s.

Step-by-step explanation:

To find the speed of the lighter skater, we can use the principle of conservation of momentum. Since the skaters are pushing off against each other, the total momentum before and after the push will remain the same. Let's denote the mass of the heavier skater (775 N) as m1 and the speed of the heavier skater as v1. We can also denote the mass of the lighter skater (655 N) as m2 and the speed of the lighter skater as v2. Using the equation:

m1v1 + m2v2 = m1v1' + m2v2'

where v1' and v2' are the final speeds after the push, we can solve for v2' (the speed of the lighter skater) as follows:

(775 N)(1.60 m/s) + (655 N)(0 m/s) = (775 N)(0 m/s) + (655 N)(v2')

Simplifying the equation, we get:

1240 + 0 = 0 + 655v2'

v2' = 1240/655 = 1.89 m/s