Question

A ball is thrown from an initial height of 7 feet with an initial upward velocity of 28/fts . The ball's height h (in feet) after t seconds is given by the following. =h+7−28t16t2 Find all values of t for which the ball's height is 15 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

Answer 1

To determine when the ball reaches a height of 15 feet, we solve the quadratic equation 16t^2 - 28t + 8 = 0 using the quadratic formula, yielding two times: approximately 0.54 seconds and 3.79 seconds.

Step-by-step explanation:

To find all values of t for which the ball's height is 15 feet, we need to set the given quadratic height function equal to 15 and solve for t. The height function was given as h(t) = 7 + 28t - 16t2, which we set to 15:

15 = 7 + 28t - 16t2

This simplifies to:

16t2 - 28t + 8 = 0

Using the quadratic formula, t is found to be approximately 3.79 seconds and 0.54 seconds. The ball reaches 15 feet twice during its flight: once on the way up and once on the way down. We round the answers to the nearest hundredth as requested.

Answer 2

1 minute is the answer.