(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A skier of mass 70 kg sets off, with initial speed of 5 m(s^-1), down the line of greatest slope of an artificial ski-slope. The ski-slope is 80 metres long and is inclined at a constant angle of 20° to the horizontal. During the motion the skier is to be modelled as a particle.

- Ignoring air resistance and friction, calculate the speed of the skier at the bottom of the slope.

- The skier actually reaches the bottom of the slope with speed 6 m(s^-1). Calculate the magnitude of the constant resistive force along the slope which could account for this final speed.

2. Relevant equations

3. The attempt at a solution

For the first question my work looks like this:

(Total energy at the top of the slope) = (total energy at the bottom of the slope)

=> (PE at the top of the slope + KE at the top of the slope) = (PE at the bottom of the slope + KE at the bottom of the slope)

=> ((70g x 80sin20) + (0.5 x 70 x 5^2)) = (0 + (0.5 x 70 x v^2))

Taking g=10

=> v = sqrt(((56000sin20) + (35 x 25))/35) = 23.9 m(s^-1) (to 3 s.f.)

However, the correct answer is 23.4 m(s^-1)

For the second question my work looks like this:

(PE + KE) at the top of the slope - (80F) = (PE + KE) at the bottom of the slope

Where F is the constant resistive force

This gives (56000sin20) + (35 x 25) – 80F = 35 x 36

=> 80F = (56000sin20) + (35 x 25) – (35 x 36)

=> F = ((56000sin20) + (35 x 25) – (35 x 36))/80

=> F = 234.6 N (to 1 d.p.)

However, the correct answer is 224 N newtons (to 3 s.f. probably).

What am I missing here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Total energy, speed, resistive force

**Physics Forums | Science Articles, Homework Help, Discussion**