Question

We throw an object upward from the top of a 1280 feet tall building. The vertical position h of the object, (measured in feet) t seconds after we threw it is

h = 16t² + 256t + 1280
How long does it take for the object to hit the ground?

Answer 1

The object takes approximately 3.79 seconds to hit the ground.

Step-by-step explanation:

The equation h = 16t² + 256t + 1280 represents the vertical position of the object thrown upward from the top of a 1280 feet tall building, measured in feet, t seconds after it was thrown. To find the time it takes for the object to hit the ground, we need to determine when the height h is equal to zero.

By setting the equation equal to zero, we get 16t² + 256t + 1280 = 0. Solving this quadratic equation will give us the time it takes for the object to hit the ground. The positive root of the equation represents the time we are interested in, since the negative root represents when the ball passes by the top of the building moving downward.

Using the quadratic formula, we find that the positive root of the equation is approximately t = 3.79 seconds. Therefore, it takes approximately 3.79 seconds for the object to hit the ground.