Question

A building is known to be 256 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 = 256 - 16t²?

Answer 1

To find the time it takes for the ball to hit the ground, solve the equation h = 256 - 16t² for t. The time it takes for the ball to hit the ground is approximately 4 seconds.

Step-by-step explanation:

To find the time it takes for the ball to hit the ground, we need to solve the equation h = 256 - 16t² for t, where h is the height of the ball at time t. When the ball hits the ground, its height h will be 0. So, we have:

0 = 256 - 16t²

Simplifying this equation, we get:

16t² = 256

Dividing both sides of the equation by 16:

t² = 16

Taking the square root of both sides:

t = ±√16

Since we are interested in the time it takes for the ball to hit the ground, the time cannot be negative. Therefore, the time it takes for the ball to hit the ground is:

t ≈ 4 seconds