Question

A roller coaster starts at rest from a height of 110m, and accelerates down the track to a height of 10m. Find the speed it can reach, assuming no friction.

Answer 1

$v^{2}$ = $u^{2}$ + 2ar
$v^{2}$  = 0 + 2 * 9.8 m/s * (110 m - 10m)
v = $\sqrt{1960}$ = 44 m/s
if it is going down vertically. if there is some angle - it would be another story

Answer 2

Answer: The final velocity of the roller coaster is 44.3 m/s

Explanation:

To calculate the final velocity of the roller coaster, we use third equation of motion:

$v^2-u^2=2as$

where,

s = distance traveled = 110 - 10 = 100 m

u = initial velocity of the roller coaster = 0 m/s

v = final velocity of the roller coaster = ? m/s

a = acceleration due to gravity = $9.8m/s^2$

Putting values in above equation, we get:

$v^2-(0)^2=2\times 9.8\times 100\\\\v=\sqrt{1960}=44.3m/s$

Hence, the final velocity of the roller coaster is 44.3 m/s