Question

8.) A toy rocket is fired upward from the ground. The relation between its height h, in feet, and the time t from launch, in seconds, can be described by the function h(t) = -6t2 + 64t.

a. Determine if the rocket will reach 80 feet. Explain how you know whether it will reach that height.
How long does the rocket stay more than 48 feet above the ground? Explain how you reached your

Answer 1

To determine if the toy rocket reaches 80 feet, we solve the equation -6t^2 + 64t = 80. To find the duration the rocket stays above 48 feet, we solve the inequality -6t^2 + 64t > 48.

Step-by-step explanation:

The toy rocket's height as a function of time can be modeled by the quadratic equation h(t) = -6t2 + 64t. To determine if the rocket will reach 80 feet, we set the function equal to 80 and solve for t:

80 = -6t2 + 64t

Solving this quadratic equation will let us know whether there are positive real solutions, which would indicate the times at which the rocket reaches 80 feet.

To find out how long the rocket stays above 48 feet, we solve the inequality -6t2 + 64t > 48. This will give us the range of time values for which the rocket's height is greater than 48 feet.