Question

Jivesh 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 time t = 0, where t is measured in seconds. For Jivesh's Model A rocket, he uses the equation h = −40t2 + 120t. When is the height of the Model A rocket 90 centimeters? Round your answers to the nearest hundredth. After t ≈ seconds, the rocket will have reached a height of 90 centimeters.

Answer 1

After 1.5 seconds, the rocket will have reached a height of 90 centimeters.

Explanation:

You know that for Jivesh's Model A rocket, he uses the equation:

h = −40*t² + 120*t

You want to know at what time the height of the model A rocket is 90 centimeters, that is, at what time t the height of the rocket h has a value of 90. Substituting this value in the equation you obtain:

90= −40*t² + 120*t

A quadratic equation has the general form:

a*x² + b*x +c= 0

where a, b and c are known values ​​and a cannot be 0.

Taking the equation for Jivesh's model A rocket to that form, you get:

-40*t² +120*t - 90= 0

The roots of a quadratic equation are the values ​​of the unknown that satisfy the equation. And solving a quadratic equation is finding the roots of the equation. For this you use the formula:

`\frac{-b+-\sqrt{b^(2)-4*a*c } }{2*a}`

In this case, solving the equation is calculating the values ​​of t, that is, you find the moment when the rocket will have reached a height of 90 centimeters.

Being a= -40, b=120 and c= -90, then

`\frac{-120+-\sqrt{120^(2)-4*(-40)*(-90) } }{2*(-40)}`

`(-120+-√(14,400-14,400) )/(2*(-40))`

`(-120+-√(0) )/(2*(-40))`

`(-120+-0 )/(2*(-40))`

`(-120 )/(2*(-40))=(-120)/(-80) =1.5`

This means that after 1.5 seconds, the rocket will have reached a height of 90 centimeters.