Question

Immediately after your final exams, you fly to Jackson Hole for some winter skiing. You start from rest at the top of a L = 100 meter slope, angled at 10° above horizontal. At the end of the slope is a cliff h = 20 meters above ground level. Ignore friction. • (a) How far from bottom of the cliff will you land? • (b) What is your velocity v just before you hit the ground?

Answer 1

here,

the length of incline , l = 100 m

theta = 10 degree

a)

the speed of ski before the launch , v = sqrt(2 * g * l * sin(10))

v = sqrt(2 * 9.81 * 100 * sin(10))

v = 18.5 m/s

for vertical direction

let the time taken to hit the floor be t

h = u * sin(theta) * t + 0.5 * g * t^2

20 = 18.5 * sin(10) * t + 0.5 * 9.81 * t^2

solving for t

t = 1.72 s

the horizontal distance , x = u * cos(theta) * t

x = 18.5 * cos(10) * 1.72 m

x = 31.3 m

b)

let the speed of ski at the bottom be v

using conservation of energy

0.5 * m * u^2 + m * g * h= 0.5 * m * v^2

0.5 * 18.5^2 + 9.81 * 20 = 0.5 * v^2

solving for v

v = 27.1 m/s

the speed before hitting yhe ground is 27.1 m/s