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. ?

Question

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?

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Answer 1 · 2015-11-21T18:17:54

(a)

#2.97"m"#

(b)

There will be no effect.

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

Potential energy = kinetic energy

#:.cancel(m)gh=1/2cancel(m)v^2#

#:.v=sqrt(2gh)#

#v=sqrt(2xx9.8xx25)=22.13"m/s"#

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

#v^2=u^2-2gh#

#:.0=(22.13sin20)^2-2xx9.8xxh#

#:.h=58.17/19.6=2.97"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.