You begin sliding down a 10° ski slope. Ignoring friction and air resistance, how fast will you be moving after 6.4 s? Round to two decimal places and report your answer in SI units.

Answer 1

There are a few ways to think about this problem, but I'll give you what I think is the most straightforward.

You likely know that if this person were just dropped in the air, their acceleration would be a = g = 9.81 m/s². This is the same as if the slope were 90^o. And obviously if the surface were flat, or 0^o, they would not move and their acceleration would be 0. This is due to the normal force that the ground is providing, which counters the force of gravity. The bigger the slope, the closer to 9.81 m/s² their acceleration will be.

To find the skier's acceleration, try this:

1. Draw an arrow pointing down, labeled 9.81 m/s²
2. Now, from the top of that arrow, draw the ski slope. So there's an 80^o angle between the first arrow and the second.
3. Draw a diagonal line from the bottom of your 9.81 m/s² vector so that it intersects your slope line perpendicularly. You now have a right triangle with 9.81 m/s² as the hypotenuse.
4. We're going to break the acceleration due to gravity down into perpendicular components to suit our needs here. I usually call them a_parallel and a_{perpendicular} . The parallel part is what we need to do the problem. The perpendicular part is ignored -- even though gravity is pulling us down into the ski slope, this is cancelled out by the normal force.
5. Use your trigonometry formulas to find that short side of the triangle that represents a_parallel.
6. You know all 3 angles and you know the hypotenuse, so either sin or cos formulas will work - your choice.

OK now we know the acceleration down the slope, finding the speed is pretty straightforward:

1. Choose a 1-d motion formula that includes "a" and "t" (since you know them both), and also include v_f (since that's what you're solving for). Remember that we also know that v_i = 0 m/s, because it says "You begin sliding" in the problem.
2. The simplest formula for this is v_f = v_i + at. Just plug in what you know, solve for v_f, and round your answer to 2 decimals.