The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = -16t2 + 96t, where t is the time in seconds. How long will it take the object to reach a height of 144 feet?
To find out how long it will take the object to reach a height of 144 feet, we can set up the equation:
h = 144
Substituting the formula for height:
-16t^2 + 96t = 144
Now we need to solve this quadratic equation for t. To do that, we can rearrange the equation to the standard quadratic form:
-16t^2 + 96t - 144 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -16, b = 96, and c = -144. Plugging in these values, we get:
t = (-96 ± √(96^2 - 4(-16)(-144))) / (2(-16))
Simplifying further:
t = (-96 ± √(9216 - 9216)) / (-32)
Since the discriminant (b^2 - 4ac) is zero, the quadratic equation has only one root. Therefore, we can simplify the equation to find the time it takes for the object to reach a height of 144 feet:
t = -96 / (-32)
t = 3 seconds
So, it will take the object 3 seconds to reach a height of 144 feet.