Question

A roller coaster starts at 2.5m/s at a height of 25m above the ground. Determine the speed of the roller coaster when it is:

a. 20m above the ground;

b. 10m above the ground;

c. At ground level.

Answer 1

Answer

Initial speed

u=2.5 m/sec

Height H=25m

The initial kinetic energy of roller coaster

$KE_i=\frac{mu^2}{2}$

Final kinetic energy

$KE_f=\frac{mv^2}{2}$

a) using energy conservation

mg(H-h) =$\frac{mv^2}{2}-\frac{mu^2}{2}$

So speed of roller caster at 20m

$v=\sqrt{u^2+2g(H-h)}\\=\sqrt{25\times25+2\times9.8\times5}\\=26.89m/s$

b) at height h=10m

So speed

$v=\sqrt{u^2+2g(H-h)}\\=\sqrt{25\times25+2\times9.8\times15}\\=30.31m/s$

c) at ground level

$v=\sqrt{u^2+2gH}\\=\sqrt{25\times25+2\times9.8\times25}\\=33.39m/s$