Question

A roller coaster is traveling at 5 m/s at the top of a hill 40 m above the ground. What is the speed of the roller coaster when it is 15 m above the ground?

Answer 1

Given: $h_1 = 40\,m, v_1 = 5\,\frac{m}{s}, h_2 = 15\,m$

Find: $v_2$

Solution:

$$\begin{array}{l} \text{Initial P.E. + K.E. = } mgh_1 + \frac{mv_1^2}{2} = \\ = 40\,mg + 0.5 \cdot 25\,m = 40\,mg + 12.5\,m \end{array}$$ $$\begin{array}{l} \text{Final P.E. + K.E. = } 15\,mg + \frac{mv_2^2}{2} \\ \text{Initial P.E. + K.E. = Final P.E. + K.E.} \\ 40\,mg + 12.5\,m = 15\,mg + \frac{mv_2^2}{2} \\ v_2 = 22.7\,m/s \end{array}$$

Answer:

$$v_2 = 22.7\,m/s$$