Question

A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by d = -16t^2 - 2t + 515. To the nearest tenth (one decimal), how long after the rock is thrown is it 410 feet from the ground?

a) 2.8 seconds
b) 3.6 seconds
c) 4.2 seconds
d) 5.0 seconds

Answer 1

The rock is 410 feet from the ground 2.8 seconds after it is thrown, which is found by solving the quadratic equation derived from the given distance function with the distance set to 410 feet.

Step-by-step explanation:

To find out how long after the rock is thrown it is 410 feet from the ground, we need to solve the quadratic equation for t given by d = -16t^2 - 2t + 515, where d is set to 410 feet to reflect the desired distance from the ground. Setting the equation to 410 gives us 410 = -16t^2 - 2t + 515, which simplifies to 0 = -16t^2 - 2t + 105. Using the quadratic formula, we find that the roots of the equation are approximately t = 2.8 s and t = -1.8 s. Since time cannot be negative in this context, the correct answer is t = 2.8 s to the nearest tenth, which corresponds to option a).