# A 59 kg skier starts from rest at height H = 25 m above the end of a ski-jump ramp (see the figure). As the skier leaves the ramp, his velocity makes an angle of θ = 20° 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 10 kg backpack, what would h be? Nov 21, 2015

(a)

$2.97 \text{m}$

(b)

There will be no effect.

#### Explanation:

To find his velocity at the end of the ramp we can use the conservation of energy:

Potential energy = kinetic energy

$\therefore \cancel{m} g h = \frac{1}{2} \cancel{m} {v}^{2}$

$\therefore v = \sqrt{2 g h}$

$v = \sqrt{2 \times 9.8 \times 25} = 22.13 \text{m/s}$

Now we can get $h$ by considering the vertical component of his velocity:

${v}^{2} = {u}^{2} - 2 g h$

$\therefore 0 = {\left(22.13 \sin 20\right)}^{2} - 2 \times 9.8 \times h$

$\therefore h = \frac{58.17}{19.6} = 2.97 \text{m}$

(b)

You can see that $m$ does not feature in any of this so carrying a backpack will have no effect. Think of Galileo's famous experiment.