Audrey launches a toy rocket from a platform. The height of the rocket in feet is given by h, equals, minus, 16, t, squared, plus, 16, t, plus, 140h=−16t
2
+16t+140 where tt represents the time in seconds after launch. How long is the rocket in the air?
To find out how long the rocket is in the air, we need to determine the time at which the rocket reaches the ground. This occurs when the height of the rocket is equal to 0.
So, we set h = 0 in the equation:
0 = -16t^2 + 16t + 140
Simplify:
16t^2 - 16t - 140 = 0
Divide by 4 to simplify:
4t^2 - 4t - 35 = 0
Now we can solve for t using the quadratic formula:
t = (-(-4) ± √((-4)^2 - 4*4*(-35))) / (2*4)
t = (4 ± √(16 + 560)) / 8
t = (4 ± √576) / 8
t = (4 ± 24) / 8
Therefore, t = (4 + 24) / 8 or t = (4 - 24) / 8
t = 28 / 8 or t = -20 / 8
t = 3.5 seconds or t = -2.5 seconds
Since time cannot be negative, the rocket is in the air for 3.5 seconds.