Question

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

Answer 1

A) The 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:
$v=\sqrt{\frac{2U}{m}}=\sqrt{\frac{2\cdot 1000 J}{60.0 kg}}=5.8 m/s$