One more problem.?

Question

A skier starts from rest at the top of a 45 m high hill, skis down a 30 degree incline to valley and continues up a 40 m hill. The heights of both hill are measured from the valley floor. Assume you can neglect friction and the effect of ski poles. How fast is the skier moving at the bottom of the valley? What is the skiers speed at the top of the next hill? Would the angles of the hills affect your answers?

Answer 1

This is a variation on Galileo. He didn't have access to accurate clocks, so he "slowed down" the fall of objects by rolling/sliding them down a ramp.
The acceleration (g) down a ramp is determined by the cosine of the ramp angle. A 30 degree angle means a factor of 0.5.

If the height is 45m and the angle is 30 degrees, the LENGTH is 51.96m. Using d = 1/2 at^2 Solving for t^2 gives 21.2, or t= 4.6 seconds

Using v= at, = 0.5*9.81*4.6 = 11.3 m/sec

The speed at the top of the 40m hill is the same as the speed after travelling down 5m, or along 5.77m
Using the methods above, the smaller trip took 1.53 seconds, for a velocity of 3.76 m/sec

Oh and yes- steeper hills would attenuate gravity less, so stteper hills give faster speeds. A 60 degree slope would be 0.866*gravity.

You may want to double check my figures!

Answer 2

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Answer 3

the last question, yes