Question

A toy rocket is launched upward from ground level with an initial velocity of 47 meters per second. Its height is a function of ​time, given by h= -4.9t²+47t, where h represents the height in meters and t represents the time in seconds. What is the maximum height reached by the rocket and how long is it in​ flight?

Answer 1

The maximum height of the toy rocket is determined using the vertex of the parabolic equation representing its flight, and the time in flight is found when the height equals zero.

Step-by-step explanation:

To determine the maximum height reached by the toy rocket and the total time in flight, we will analyze the given quadratic equation h = -4.9t² + 47t representing the rocket's height as a function of time during its flight. The maximum height is achieved at the vertex of the parabola described by this equation. The vertex form of a parabola is h = a(t-h)² + k, where (h, k) is the vertex of the parabola. To find the time t at the maximum height, we apply the formula t = -b/(2a), which in this context is t = -47 / (2 * -4.9), giving us the time at max height.

To find the total time in flight, we solve for when h=0, which is when the rocket hits the ground again. We use the quadratic formula or factor the quadratic equation if possible to find the time when the rocket is back on the ground. The rocket is in flight until its height h is zero.