Question

A person throws a stone into the air. The height, in feet, h(t) after t seconds is given by the following equation: h(t) = -16t^2 + 64t + 19. When is the stone at a height of 39 feet?

A. t = 0.5 seconds
B. t = 2 seconds
C. t = 3.5 seconds
D. t = 4 seconds

Answer 1

To find when the stone is at 39 feet, we solve for t in the quadratic equation obtained by setting the height equation equal to 39. The solution results in two possible times, t = 0.5 seconds and t = 2 seconds. Based on the given options, the stone is at the height of 39 feet at t = 2 seconds.

Step-by-step explanation:

To determine when the stone is at a height of 39 feet, we need to set the equation h(t) = -16t2 + 64t + 19 equal to 39 and solve for t. This gives us the quadratic equation -16t2 + 64t + 19 = 39. Subtracting 39 from both sides simplifies the equation to -16t2 + 64t - 20 = 0.

By using the quadratic formula, t = ∛{-b ± √{b2 - 4ac}}/{2a}, where a = -16, b = 64, and c = -20, we find the values of t that satisfy the equation:

∛{64 ± √{642 - 4(-16)(-20)}}/{2*(-16)}

which simplifies to: ∛{64 ± √{4096 - 1280}}/{-32}

We then find two possible times t when the height is 39 feet, these are t = 0.5 seconds and t = 2 seconds. However, since the question gives us specific options to choose from, we match our results to the given options and conclude that the stone is at a height of 39 feet at option B: t = 2 seconds.