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.
y = -16x² + 153x +98

Answer 1

The time that the rocket will hit the ground is approximately 6.13 seconds.

Step-by-step explanation:

The equation given to represent the height of the rocket at a given time is y = -16x² + 153x +98.

To find the time that the rocket will hit the ground, we need to determine the value of x when y equals zero.

We can set the equation equal to zero and solve for x:

0 = -16x² + 153x + 98

Using factoring, the equation can be written as:

0 = (-8x + 49)(2x + 2)

Setting each factor equal to zero, we find that x can equal 49/8 or -1.

Since time cannot be negative, we discard the negative value.

Therefore, the time that the rocket will hit the ground is 49 / 8 (approximately 6.13 seconds) to the nearest hundredth of a second.