# Haven't been able to solve can someone help me set it up?

In a ski competition, skiers first slide down a slope of 10 degrees and then encounter a horizontal section. the coefficient of friction along the slope is 0.15 and the horizontal section is frictionless. in order to slow down, a skier with a mass of 80.0kg decides to collide with a stationary cushioned block with a mass of 50.0kg. the skier sticks to the block and they slide together with a final velocity of 5.5 m/s. the skier and block then collide with a spring and it compresses 1.60m.

(a) what is the velocity of the skier before colliding with the block?

(b) determine the length of the ski slope?

(c) what is the spring constant of the spring?

### 1 Answer

- ?Lv 72 months ago
For the collision use conservation of momentum. You know the two masses, the final speed of both, and the initial speed of the block.

For the spring question use conservation of energy. A 130 kg object traveling at 5.5 m/s is brought to a stop by compressing a spring 1.6 m.

The slope question is more complicated. Draw your coordinate system at 10 degrees so that the ski slope becomes your x-axis and your y-axis is perpendicular to the slope.

That puts the normal force in the y direction and friction in the x direction as usual. Use trigonometry to calculate the x- and y-components of gravity. The net force in the y direction needs to be zero (the skier does not leave the sloped ground). Put all this together to calculate the net force in the x direction.

You know from (a) the skier's final speed at the bottom of the slope. Calculate the distance over which the force had to be exerted to accelerate the skier up to that speed.