Final answer:
To find the time a rocket launched from a tower will hit the ground, given the equation y = -16x² + 141x + 67, we set y to zero and solve the resulting quadratic equation for the non-zero value of x.
Step-by-step explanation:
The student is asking for the time it will take for a rocket to hit the ground after being launched from a tower. Given the equation y = -16x² + 141x + 67, which depicts the height (y) of the rocket as a function of time (x), we can determine the time the rocket will hit the ground by setting y to zero and solving for x, as y represents the height above the ground. To find the time the rocket reaches the ground, we want the height (y) to be zero.
Setting the equation to zero gives us the quadratic equation:
0 = -16x² + 141x + 67. Solving this equation for x will give us two solutions: one for the launch time, which is x = 0, and one for the time it will hit the ground. We will use the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), to solve for x.
Plugging in the values from the equation, we get:
a = -16, b = 141, and c = 67. After performing the calculations, we find the non-zero value of x to be the time when the rocket hits the ground. This time should be calculated to the nearest 100th of a second to provide a precise answer to the student's question.