In a downhill ski race, surprisingly, little advantage is gained by getting a ru

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 in m/s and the time taken in seconds for a skier who skies 63.0 m along a 28° slope neglecting friction for the following two cases. (Enter the final speeds to at least one decimal place.)

(a)starting from rest

final speed ? ___________ m/s

time taken? ______________ s

(b)

starting with an initial speed of 3.00 m/s

final speed? _________m/s

time taken ?___________s

Explanation / Answer

Given: s= 63 m

acceleration down the slope, a = 9.81 × sin(28) m/s2

a = 4.61 m/s2

a) Using equation of motion :

V = u+at ..............(1)

s= ut+ (1/2)at2.............(2)

V is the final speed ,

u is the initial speed,

Starting from rest means that , initial velocity u = 0

Hence from equation (2)

63 = 0+ (1/2) (4.61)(t2)

t2= 27.33 , t = 5.23 s

From equation (1)

V= u+at

v = 0+(4.61)(5.23) = 24.11 m/s

B) Using equation of motion :

v2= u2+2as

u = 3m/s

v = [ (3)2+(2×4.61×63)]

= 24.29 m/s

now using equation: v = u+at

24.29 = 3+ (4.61)t

t = 2.15 s

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