Question

What is the maximum speed when the conditions are mass =450 kg, initial height= 30 m, and the roller coaster is initially at rest?

A. 30 m/s
B. 24.2 m/s
C. 93.9 m/s
D. 132, 300 m/s

Answer 1

1. 24.2 m/s

2. 20.4 m

3. 22.5 m/s

4. 109,375 J

5. It is easy to calculate new scenarios.

Step-by-step explanation:

5/5 on the Maximum Energy Quick Check

Answer 2

B. 24.2 m/s

Step-by-step explanation:

Given;

mass of the roller coaster, m = 450 kg

height of the roller coaster, h = 30 m

The maximum potential energy of the roller coaster due to its height is given by;

`P.E_(max) = mgh\\\\PE_(max) = 450 *9.8*30\\\\PE_(max) = 132,300 \ J`

`P.E_(max) = K.E_(max) \ (law \ of \ conservation\ of \ energy)`

`K.E_(max) = (1)/(2)mv_(max)^2\\\\ v_(max)^2 = (2K.E_(max))/(m)\\\\ v_(max)^2 = (2*132300)/(450)\\\\ v_(max)^2 =588\\\\v_(max) = √(588)\\\\ v_(max) = 24.2 \ m/s`

Therefore, the maximum speed of the roller coaster is 24.2 m/s.