Question

An object is dropped from 46 feet below the tip of the pinnacle atop a 530 -ft tall building. The height h of the objoct after t seconds as ghven by the equation h=−16T² +484. Find how many seconds pass before the objoct reaches the ground.

Answer 1

Solving the quadratic equation h = -16t² + 484 by setting h to 0 for the object hitting the ground, we find that the object takes 5.5 seconds to reach the ground.

Step-by-step explanation:

To find out how many seconds pass before the object reaches the ground, we need to solve the quadratic equation representing the height h of the object after t seconds, given by the equation h = -16t² + 484. Since we want to find the time when the object hits the ground, we set h to 0 and solve for t:

0 = -16t² + 484

Now we divide by -16:

0 = t² - 30.25

To solve this quadratic equation, we take the square root of both sides:

t = √30.25

The positive root gives us the time:

t = 5.5 seconds

Therefore, it takes 5.5 seconds for the object to reach the ground.