Question

A 2430 pound roller coaster starts from rest and is launched such that it crests a 105 ft high hill with a speed of 59 mph. The roller coaster travels 396 ft in reaching the top of the hill and there is a constant drag force of 85 pounds. Determine launch energy

Answer 1

Step-by-step explanation:

Given

Weight of roller coaster is
`W=2430\ pound`

mass of roller coaster
`m=(W)/(g)=(2430)/(32.2)=75.45`

Distance traveled by roller coaster
`d=396\ ft`

drag force
`f_d=85\ pounds`

velocity at top
`v=59 mph\approx 86.53\ ft/s`

Suppose E is the initial energy

Conserving Energy at bottom and top

`E=(1)/(2)mv^2+mgh+f_d\cdot d`

`E=0.5* 75.45* 86.53^2+2430* 105+85* 396`

`E=2.9* 10^5\ foot-pound`