Question

A building is known to be 320 feet tall. A ball is dropped from the top of the building. In how many seconds will the ball hit the ground if the formula for the height of the ball at t seconds is given by h = 320 - 16t²? Step 2 of 2: In how many seconds will the ball hit the ground? Completely reduce the answer in radical form, as necessary.

Answer 1

The ball will hit the ground in approximately √(80) / 2 seconds.

Step-by-step explanation:

The formula for the height of the ball at t seconds is given by h = 320 - 16t². To find the time it takes for the ball to hit the ground, we need to solve for t when h = 0. So, we set the equation 320 - 16t² = 0. We can solve this quadratic equation using the quadratic formula. The positive root is the time it takes for the ball to hit the ground.

t = (-b ± √(b² - 4ac)) / (2a)

For the equation 320 - 16t² = 0, a = -16, b = 0, and c = 320. Plugging these values into the quadratic formula, we get:

t = (-0 ± √(0 - 4(-16)(320))) / (2(-16))

t = (√(4 * 16 *320)) / 32

Simplifying further, we get:

t = (√(20480)) / 32

t = (√64 * √320) / 32

t = 8 * √(320) / 32

t = √(320) / 4

Finally, we have:

t = √(80) / 2

Therefore, the ball will hit the ground in approximately √(80) / 2 seconds.