Question

In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 65.0 m along a 30° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)(a) starting from restfinal speed...................m/stime taken.....................s (b) starting with an initial speed of 3.00 m/s final speed..................m/stime taken .................s

Answer 1

Step-by-step explanation:

Using equation of motion

v² = u² + 2as where a = g sinθ, v is final speed and u is initial speed

u = 0 since it is starting from rest

v² = 2 × 65 × 9.8 × sin 30° = √ 637 m²/s² = 25.24 m/s

t, time taken

s = ( v+u)/2 × t

t = 2 s / ( v+ u) = 2× 65 / 25.24 = 5.151 s

b) u = 3.0 m/s

v² = 3² + 2sgsinθ = 9 + (2×65×9.8×sin 30) = 646

v = √646 m²/s²= 25.42 m/s

average velocity = (25.42 m/s + 3 m/s ) / 2 = 14.21 m/s

t = d / average speed = 65 m / 14.21 m/s = 4.574 s