Question

A roller coaster's height is given by the equation h = -0.025t^2 + 4t + 50, where t represents thetime in seconds. How long will it take riders to pass over the hill and reach ground level? Hint:Set h = 0.

Answer 1

Answer: 171.65 seconds.

Step-by-step explanation

Given

`h=-0.025t^2+4t+50`

Procedure

We are asked how long will it take riders to pass over the hill and reach ground level, algebraically meaning when does h = 0. By rewriting our equation we get:

`0=-0.025t^2+4t+50`

In this case, we have a function in the form ax² + bx + c = 0. These types of equations can be solved by using the General Quadratic Formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

where a, b and c represents the coefficients in the form of the equation ax² + bx + c =0. In our case:

• a = - 0.025

,

• b = 4

,

• c = 50

By replacing the values and simplifying we get:

`x=(-4\pm√((4)^2-4(-0.025)(50)))/(2(-0.025))`
`x=(-4\pm√(16+5))/(-0.05)`
`x=(-4\pm√(21))/(-0.05)`

Now, we have two solutions:

`x_1=(-4+√(21))/(-0.05)=-11.65`
`x_1=(-4-√(21))/(-0.05)=171.65`

As we cannot have a negative time, then it will take 171.65 seconds.