A rock is thrown from the top of a tall building. The distance in feet between the rock and the ground t seconds after thrown is given by d = - 16t2 - 4t + 412. How long after the rock is thrown is it 407 feet from the ground?

0.448 seconds

Step-by-step explanation:

d = - 16t² - 4t + 412

find t when d = 407

substituting d = 407 into the equation:

407 = - 16t² - 4t + 412 (subtract 407 from both sides)

-16t² - 4t + 412 - 407 = 0

-16t² - 4t + 5 = 0 (multiply both sides by - 1)

16t² + 4t - 5 = 0

solving using your method of choice (i. e completing the square or using the quadratic equation), you will end up with

t = (-1/8) (1 + √21) = - 0.70 seconds (not possible because time cannot be negative)

or

t = (-1/8) (1 - √21) = 0.448 seconds (answer)