Question
A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2 +46t+6 After how many seconds will the ball hit the ground
Answers
GPT 3.5
To find out when the ball hits the ground, we need to solve for when the height (h) is equal to 0.
So, we set the equation equal to 0:
-16t^2 + 46t + 6 = 0
Next, we can solve this quadratic equation using the quadratic formula:
t = (-46 ± √(46^2 - 4(-16)(6))) / 2(-16)
t = (-46 ± √(2116 + 384)) / -32
t = (-46 ± √2500) / -32
t = (-46 ± 50) / -32
Now we find both possible solutions:
t = (4 / -32) = -1/8
t = (96 / -32) = -3
We cannot have a negative time when considering the ball hitting the ground, so we discard the negative solution. Therefore, the ball will hit the ground after approximately 3 seconds.
So, we set the equation equal to 0:
-16t^2 + 46t + 6 = 0
Next, we can solve this quadratic equation using the quadratic formula:
t = (-46 ± √(46^2 - 4(-16)(6))) / 2(-16)
t = (-46 ± √(2116 + 384)) / -32
t = (-46 ± √2500) / -32
t = (-46 ± 50) / -32
Now we find both possible solutions:
t = (4 / -32) = -1/8
t = (96 / -32) = -3
We cannot have a negative time when considering the ball hitting the ground, so we discard the negative solution. Therefore, the ball will hit the ground after approximately 3 seconds.