Question
An object is dropped from the top of a 400-ft building. The height h of the ball after t seconds is modeled by the equation h=16f^2+400. How long is the ball in the air?
Answers
GPT 3.5
To find how long the ball is in the air, we need to find the time it takes for the height of the ball to reach 0.
Given the equation h = 16t^2 + 400, we set h = 0 and solve for t:
0 = 16t^2 + 400
Dividing both sides of the equation by 16:
0 = t^2 + 25
Rearranging the equation:
t^2 = -25
Since time cannot be negative, there are no real solutions for t in this case.
Therefore, the ball is not in the air for any amount of time.
Given the equation h = 16t^2 + 400, we set h = 0 and solve for t:
0 = 16t^2 + 400
Dividing both sides of the equation by 16:
0 = t^2 + 25
Rearranging the equation:
t^2 = -25
Since time cannot be negative, there are no real solutions for t in this case.
Therefore, the ball is not in the air for any amount of time.