Question

The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding 20 m/s. find the maximum value of a allowed by these regulations.

Answer 1

The maximum speed allowed by the safety regulations is 11.4 m/s.

Step-by-step explanation:

To find the maximum speed allowed by the safety regulations for the roller coaster, we can use the formula for centripetal acceleration:

a = v^2 / r

where a is the acceleration, v is the velocity, and r is the radius of curvature. In this case, the downward acceleration of the car due to gravity is 1.50 times the acceleration due to gravity. So we can use the equation:

1.50g = v^2 / r

Solving for v, we get:

v = sqrt(1.50g * r)

where g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we have:

v = sqrt(1.50 * 9.8 * 15.0)

v = 11.4 m/s

Answer 2

maximum allowed value of the speed in roller coaster is given as

`v = 20 m/s`

now from kinematics we can say

`v^2 - v_i^2 = 2 a s`

here initial speed will be

`v_i = 0`

acceleration is due to gravity

`a = 9.8 m/s^2`

now we can use this to find the height

`20^2 - 0^2 = 2 * 9.8* h`

`400 = 19.6 *h`

`h = 20.4 m`

so maximum allowed height will be 20.4 m