Question

1. A roller coaster at an amusement park was being

evaluated for safety. It was decided that if the cars ever
reached 40 m/s then the roller coaster would be considered
unsafe.
(a)The first part of the coaster rises to a height of 70 meters
and drops to 15 meters above the ground. Is this within the
limits?

Answer 1

The roller coaster is within the limits

Step-by-step explanation:

h₁ = 70 m

h₂ = 15 m

v₁ = 0

EM₁ = EM₂

EP₁ + EK₁ = EP₂ + EK₂

mgh₁ +
`(1)/(2)`mv₁² = mgh₂ +
`(1)/(2)`mv₂²

m(gh₁ +
`(1)/(2)`v₁²) = m(gh₂ +
`(1)/(2)`v₂²)

gh₁ +
`(1)/(2)`v₁² = gh₂ +
`(1)/(2)`v₂²

9.8(70) +
`(1)/(2)`(0)² = 9.8(15) +
`(1)/(2)`v₂²

`(1)/(2)`v₂² = 9.8(70 - 15)

v₂² = 539 × 2

v₂ = √1078

= 32.83 m/s

since 32.83 < 40 m/s, therefore the roller coaster is within the limits