Question

On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a rough patch that reduces her speed by 45% due to a friction force that is 25% of her weight. Use the work‑energy theorem to find the length of this rough patch.

Answer 1

Answer: 1.25 m

Step-by-step explanation:

Given

initial velocity
`(v_i )=3 m/s`

Final velocity
`(v_f)=0.55* 3=1.65 m/s`

Change in kinetic Energy =work done by Friction

change in Kinetic Energy
`=(m)/(2)\left ( v_i^2-v_f^2\right )`

work done by friction
`=\mu mgL`

`(m)/(2)\left ( 3^2-1.65^2\right )=0.25\cdot mg* L`

`3.135=0.25* 9.8* L`

L=1.25