Question

Problem 6: 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 62.5 m along a slope that is 25°, measured from horizontal, in the following situations (you may neglect friction).

Answer 1

Step-by-step explanation:

Given that,

Distance covered by the skier, d = 62.5 m

Slope from the horizontal,
`\theta=25^(\circ)`

Let v is the final speed of the skier. Using the third equation of kinematics as :

`v^2=u^2+2ad`

Here,
`a=g\ sin\theta` and u = 0

`v^2=2g\ sin\thetad`

`v=√(2g\ sin\theta d)`

`v=√(2* 9.8* \ sin(25)* 62.5)`

v = 22.75 m/s

The final speed of a skier is 22.75 m/s.

Let t is the time taken. Using the first equation of motion as :

`t=(v-u)/(g\ sin\theta)`

`t=(22.75)/(9.8* \ sin(25))`

t = 5.49 seconds

Hence, this is the required solution.