Question

The roller coaster from problem #1 then tops a second hill at 15.0 m/s, how high is the second hill?

Answer 1

Answer

a) Top speed of the roller coaster, v = 15 m/s

Maximum height reached by the roller coaster, h = ?

Using conservation of energy

$\dfrac{1}{2}mv^2 = m gh$

$h = \dfrac{v^2}{2g}$

$h = \dfrac{15^2}{2\times 9.81}$

$h= 11.47\ m$

b) Maximum height, H = 80 m

Top speed of the roller coaster, v = ?

Using conservation of energy

$\dfrac{1}{2}mv^2 = m gh$

$v = \sqrt{2gh}$

$v = \sqrt{2\times 9.81\times 80}$

$v = 39.62\ m/s$