Question

A rocket is launched 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 this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.

equation:
y=-16x²+186x+75

Answer 1

The time that the rocket will hit the ground, to the nearest 100th of second, is approximately 7.06 seconds.

Step-by-step explanation:

To find the time that the rocket will hit the ground, we set the equation y = -16x² + 186x + 75 equal to 0, as the rocket will hit the ground when y is equal to 0. So, we have -16x² + 186x + 75 = 0. To solve this quadratic equation, we can either factor it or use the quadratic formula. Using the quadratic formula, we have:

x = (-b ± sqrt(b² - 4ac)) / (2a)

Plugging in the values from the equation, we get:

x = (-186 ± sqrt(186² - 4(-16)(75))) / (2(-16))

Simplifying further, we have:

x = (-186 ± sqrt(34596)) / -32

Using a calculator, we find two approximate solutions for x: x = 1.58 seconds and x = 7.06 seconds. However, since we are looking for the time that the rocket hits the ground, we only consider the positive solution, which is x = 7.06 seconds. Therefore, the time that the rocket will hit the ground, to the nearest 100th of a second, is approximately 7.06 seconds.