Question

You are on roller blades on top of a mole hill. Your PE is equal to 1,500.0 joules. The last time you checked your mass was 50.0 kilograms.What is your weight in newtons? 'What is the height of the hill?If 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?

Answer 1

Given data

*The given potential energy is U_p = 1500.0 J

*The given mass is m = 50.0 kg

The weight is calculated as

$\begin{gathered} W=mg \\ =(50.0)(9.8) \\ =490\text{ N} \end{gathered}$

The formula for the height of the hill is given by the potential energy formula as

$U_p=mgh$

Substitute the known values in the above expression as

$\begin{gathered} 1500=50\times9.8\times h \\ h=3.06\text{ m} \end{gathered}$

Hence, the height of the hill is h = 3.06 m

The formula for the speed at the bottom of the hill is given by the kinetic energy formula as

$U_k=\frac{1}{2}mv^2$

Substitute the known values in the above expression as

$\begin{gathered} 1500=\frac{1}{2}(50.0)v^2^{} \\ v=7.74\text{ m/s} \end{gathered}$

Hence, the speed at the bottom of the hill is v = 7.74 m/s