Question

A ball is thrown from an initial height of 6 feet with an initial upward velocity of 27 ft/s. The ball's height h (in feet) after t seconds is given by the following. h=6+27t-16t² Find all values of t for which the ball's height is 16 feet.

Answer 1

To find the values of t when the ball's height is 16 feet, we set the equation for height equal to 16 and solve for t.

Step-by-step explanation:

To find all the values of t for which the ball's height is 16 feet, we can set the equation for height, h=6+27t-16t², equal to 16 and solve for t. So, we have:

16 = 6 + 27t - 16t²
0 = 10 + 27t - 16t²
16t² - 27t - 10 = 0

Next, we can factor or use the quadratic formula to solve this quadratic equation. After solving, we find two possible values for t: t = 0.54 and t = 3.79.

Therefore, the ball's height is 16 feet at t = 0.54 seconds and t = 3.79 seconds.