Question

1. The height of a missile t seconds after it has been fired is given by h=4.9t^2+44.1t. How many seconds will it take for the rocket to reach its greatest height?​

Answer 1

The rocket will take 4.5 seconds to reach its maximum height.

Explanation:

The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t

This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0

To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply:
`x=(-b)/(2*a)`. The y coordinate of the vertex corresponds to the function evaluated at that point.

In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:

`t=(44.1)/(2*(-4.9))`

t=4.5

The rocket will take 4.5 seconds to reach its maximum height.