Question

A ball is thrown vertically upward from the top of the building 640 feet tall with an initial velocity of 80 feet per second. Its height h, in feet, after t seconds is given by h(t)=640+80t−16t2. After how long will it take for the ball to reach its maximum height? (Round your answer to 1 decimal place.) 8.5sec 3.2sec 2.5sec 13.3sec

Answer 1

The correct answer is 2.5 sec.

Explanation:

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the quadratic function h(t) = 640 + 80t - 16t^2. The vertex represents the highest point on the graph, which corresponds to the maximum height of the ball.

The vertex of a quadratic function in the form h(t) = at^2 + bt + c can be found using the formula:

t = -b / (2a)

In this case, a = -16 and b = 80. Substituting these values into the formula, we have:

t = -80 / (2(-16))

t = -80 / (-32)

t = 2.5

Therefore, it will take the ball 2.5 seconds to reach its maximum height