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You are on roller blades on top of a small hill. Your potential energy is equal to 1,000.0 joules. The last time

you checked your mass was 60.0 kilograms.

AWhat is your weight in newtons?
BWhat is the height of the hill?
CIf you start skating down this hill, your potential energy will be converted to kinetic energy. At the

bottom of the hill, your kinetic energy will be equal to your potential energy at the top. What will be

your speed at the bottom of the hill?

Verified Answer :

skyluke89
AThe weight of a person is given by:
\(W=mg\)
where m is the mass of the person and g is the gravitational acceleration. In this problem, the mass of the person is m=60.0 kg, while the value of g is \(g=9.81 m/s^2\), therefore the weight of the person is 
\(W=(60 kg)(9.81 m/s^2)=588.6 N\)

b) The gravitational potential energy at the top of the hill is U=1000 J. The potential energy is also given by the product between the weight W and the height of the hill h:
\(U=Wh\)
If we rearrange the equation, we can calculate the height of the hill, h: 
\(h= \frac{U}{W} = \frac{1000 J}{588.6 N} =1.70 m\)

c) At the bottom of the hill, all the potential energy at the top of the hill has converted into kinetic energy:
\(U=K\)
\(U= \frac{1}{2} mv^2\)
where m is the mass and v is the speed. If we rearrange the formula, we can calculate the speed at the bottom of the hill:
\(v=\sqrt{\frac{2U}{m}}=\sqrt{\frac{2\cdot 1000 J}{60.0 kg}}=5.8 m/s\)

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