Question

Jlvesh is analyzing the flight of a few of his model rockets with various equations. In each equation, h is

the height of the rocket in centimeters, and the rocket was fired from the ground at timet = 0, where t is

measured in seconds.

Jivesh also has a more powerful Model B rocket. For this rocket, he uses the equation h=-90t4 + 300t.

When is the height of the Model B rocket 250 centimeters? Round your answers to the nearest

hundredth.

After t =

seconds, the rocket will have reached a height of 250 centimeters.

Answer 1

After t = 1.67 seconds, the rocket will have reached a height of 250 centimeters.

Explanation:

Given

`h = -90t^2 + 300t` --- correct expression

Required: When does height = 250 cm

To do this, we have:

`h = 250`

This gives:

`250 = -90t^2 + 300t`

Rewrite as:

`90t^2 - 300t + 250 = 0`

Divide through by 10

`9t^2 - 30t + 25 = 0`

Expand

`9t^2 - 15t - 15t + 25 = 0`

Factorize:

`3t(3t - 5) -5(3t - 5) = 0`

`(3t - 5)(3t - 5) = 0`

This gives:

`3t - 5 = 0`

Solve for 3t

`3t = 5`

Solve for t

`t = (5)/(3)`

`t = 1.67s`