Question

Abrocket isnlaunched from a tower. the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. using the equation, find out the time at which yhe rocket will reach its max, to the nearest 100th of a second y=-16x² + 163x + 137

Answer 1

The time at which the rocket reaches its maximum height is found using the vertex formula of a quadratic function. The time calculated is 5.09375 seconds, which is rounded to 5.09 seconds to the nearest hundredth.

Step-by-step explanation:

To find the time at which the rocket reaches its maximum height, we can use calculus or the vertex formula for a quadratic function. The equation of the rocket's height as a function of time is y = -16x² + 163x + 137. The vertex of a parabola given by y = ax² + bx + c occurs at x = -½(b/a). Substituting the values from the equation, we get x = -½(163/-16), which yields the time when the rocket reaches its maximum height. To get the maximum height itself, we would substitute this time back into the original equation. However, since we're only asked for the time, we complete the solution by evaluating the time to the nearest hundredth of a second.

Calculating this, we get:
x = -½(163/-16) = 5.09375, which to the nearest hundredth of a second is 5.09 seconds.