Speed after gliding with friction force present using work/E

[miyayeah]

Homework Statement

The question is as follows: A 50kg ice skater is gliding along the ice, heading due north at 4.0m/s. The ice has a small coefficient of static friction, to prevent the skater from slipping sideways, but kinetic friction =0. Suddenly, a wind from the northeast exerts a force of 4N on the skater. Use work and energy to find the skater's speed after gliding 100m in this wind.

Homework Equations

W= F ⋅ d
W= ΔKE = 1/2 mv_f²-1/2 mv_i²

The Attempt at a Solution

W= F ⋅ d = (sin45)(4N)(100m) = 282.842712 J
In this step I assumed the angle to be 45 degrees because we are trying to find the y component of the force. (Since there is no movement sideways and speed is not affected by the sideway movement)
I used the above value of work in the next step. I rearranged the formula below to get final velocity.

W= ΔKE = 1/2 mv_f²-1/2 mv_i²
v_f= √[(2W+mv_i²)/m]

Plugging in the values from the question gave me 5.2 m/s. The correct answer was 2.2m/s.

Any help would be much appreciated!

 

[stockzahn]

Have a look at your last equation. If you add W and the initial kinetic energy, the final velocity must be larger than the initial one.

 

[haruspex]

heading due north

a wind from the northeast

So will the skater go faster or slower?

 

[miyayeah]

So will the skater go faster or slower?

Oh I read the question wrong. Thank you, I got the right answer this time.