Question

A 57 kg skier starts from rest at a height of H = 27 m above the end of the ski-jump ramp. As the skier leaves the ramp, his velocity makes an angle of 28° with the horizontal. Neglect the effects of air resistance and assume the ramp is frictionless.
(a) What is the maximum height h of his jump above the end of the ramp?
(b) If he increased his weight by putting on a backpack, would h then be greater, less or, the same?

Answer 1

Answer:

(a)$h=5.95m$

(b) h is the same

Explanation:

According to the law of conservation of energy:

$E_i=E_f\\U_i+K_i=U_f+K_f$

The skier starts from rest, so $K_i=0$ and we choose the zero point of potential energy in the end of the ramp, so $U_f=0$. We calculate the final speed, that is, the speed when the skier leaves the ramp:

$mgH=\frac{mv^2}{2}\\v=\sqrt{2gH}\\v=\sqrt{2(9.8\frac{m}{s^2})(27m)}\\v=23\frac{m}{s}$

Finally, we calculate the maximum height h above the end of the ramp:

$v_f^2=v_i^2-2gh$

The initial vertical speed is given by:

$v_i=vsin\theta$

and the final speed is zero, solving for h:

$h=\frac{v_i^2}{2g}\\h=\frac{((23\frac{m}{s})sin(28^\circ))^2}{2(9.8\frac{m}{s^2})}\\h=5.95m$

(b) We can observe that the height reached does not depend on the mass of the skier