Question

In a downhill ski race, your final velocity is not affected very much by getting a running start, because the initial kinetic energy is small compared with the gain in gravitational potential energy on even small hills. However, you will finish the race much faster (which is more important!). To demonstrate this, find the final speed and the time taken for a skier who skies 72.5 m along a slope that is 29°, measured from horizontal, in the following situations (you may neglect friction).

Answer 1

Part a)

`v = 26.3 m/s`

Part b)

`t = 5.53 s`

Step-by-step explanation:

As we know that there is no friction on the hill

so here by energy conservation we will have

`(1)/(2)mv^2 = mgL sin\theta`

so we will have

`v^2 = 2gL sin\theta`

`v^2 = 2(9.81)(72.5) sin29`

`v^2 = 689.62`

`v = 26.3 m/s`

now in order to find the time we know that the acceleration along the surface is given as

`a = g sin29`

`a = 4.755 m/s^2`

now we have

`v_f = v_i + at`

`26.3 = 0 + 4.755 t`

`t = 5.53 s`