5. Figure 4 shows a 60 kg skier who starts from rest at a height H = 20 m above

Question

5. Figure 4 shows a 60 kg skier who starts from rest at a height H = 20 m above the end of a ski-jump ramp and leaves the ramp at angle theta = 28 degree. Neglect the effects of air resistance and assume the ramp is frictionless. a. Based on conservation of energy and the angle of the jump, what is his velocity (magnitude and angle) as he leaves the jump? b. What is the maximum height h of his jump above the end of the ramp? Note, assume the skier after he leaves the jump acts like a projectile with no drag. Calculate using conservation of energy. c. If he increased his weight by putting on a backpack, would h be greater, less or the same?

Explanation / Answer

a) m*g*H = 0.5*m*v^2

v = sqrt(2*g*H)

= sqrt(2*9.8*20)

= 19.8 m/s

b) vx = v*cos(28)

= 19.8*cos(28)

= 17.48 m/s

at maximum height, vy = 0

initial mechanical energy = final mechanical enrgy

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

h = 0.5*(v^2-vx^2)/g

= 0.5*(19.8^2 - 17.48^2)/9.8

= 4.41 m

c) same

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