Question

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function h = -16t² + 64t + 960. When did it hit the ground?

Answer 1

To find when the ball hits the ground, we set the equation h = -16t² + 64t + 960 to zero and solve for t using the quadratic formula. The calculation results in two potential times, and we take the positive value as the relevant time at which the ball reaches the ground.

Step-by-step explanation:

To determine when the ball hit the ground, we need to find when the height h is zero in the function h = -16t² + 64t + 960. To do this, we set the function equal to zero and solve for t:

0 = -16t² + 64t + 960

Solving this quadratic equation, we can use the quadratic formula:

t = −b ± √(b² − 4ac) / 2a

Here, a = -16, b = 64, and c = 960. Plugging these values into the formula, we get two possible values for t. We discard the negative time as it doesn't make physical sense in this scenario, and take the positive one as the time when the ball hits the ground. After calculating the discriminant and completing the formula, we find the time when the ball reaches the ground.