A ball falls from the top of a roof 320 feet above the ground. The formula h = -16t2 + 16t + 320 described the height of the ball above the ground, h, in feet, t seconds after the fall begins. How long will it take the ball to strike the ground?
To find the time it will take for the ball to strike the ground, we need to solve the equation h = -16t^2 + 16t + 320 for t when h is equal to zero.
Setting h to zero, we have:
0 = -16t^2 + 16t + 320
This equation is a quadratic equation in the form at^2 + bt + c = 0, where a, b, and c are constants. In our case, a = -16, b = 16, and c = 320.
To solve this quadratic equation, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0,
x = (-b ± sqrt(b^2 - 4ac)) / 2a.
Applying this formula to our equation, we have:
t = (-16 ± sqrt(16^2 - 4(-16)(320))) / 2(-16)
Simplifying further, we get:
t = (-16 ± sqrt(256 + 20480)) / -32
t = (-16 ± sqrt(20736)) / -32
t = (-16 ± 144) / -32
Now, we have two possible values for t:
1) t = (-16 + 144) / -32
t = 128 / -32
t = -4
2) t = (-16 - 144) / -32
t = -160 / -32
t = 5
Since time cannot be negative, the ball will strike the ground after 5 seconds.
Therefore, it will take the ball 5 seconds to strike the ground.