Question

The first hill of a roller coaster is 42.0 meters high. The roller coaster drops to a height of

Answer 1

Velocity = 27.2 m/s

Explanation:

The velocity at the bottom of the first hill can be determined with the change in Kinetic energy. Due to energy conversion, both the change in kinetic energy and potential energy is same when the height is changed.

So, by applying the formulas:

KE = $\frac{m v^{2}}{2}$

where KE is Kinetic energy, m is the mass and v is the Velocity.

PE = mgh

where PE is Potential energy, m is the mass, g is the gravitational force and h is the height.

Since, both the energies are equal, we can write:

PE = KE

$\frac{m v^{2}}{2}$ = mgh

v²   = 2gh

v     = $\sqrt{2 g h}$

To Substitute:

h = 42 - 4.2 = 37.8 m

g = 9.8 m/s²

So, v = $\sqrt{2 \times 9.8 \times 37.8}$

        = 27.2 m/s