The height, in feet, of a free�]falling object t seconds after being dropped from an initial height s can be found using the function h = �]16t2 + s. An object is dropped from a helicopter 784 feet above the ground. How long will it take the object to land on the ground?
0 at ground = - 16 t^2 + 784
so
t^2 = 784
t = sqrt (784)
0 at ground = - 16 t^2 + 784
so
t^2 = 784 / 16
t = sqrt (784 / 16)
49
To find the time it takes for the object to land on the ground, we need to determine when the object's height is equal to zero. In this case, the object starts at an initial height of 784 feet, and the height of the free-falling object can be found using the function h = -16t^2 + s, where t represents time in seconds.
We set h = 0, and substitute the given values:
0 = -16t^2 + 784
To solve this equation, we can rearrange it to isolate t^2:
16t^2 = 784
Next, divide both sides of the equation by 16:
t^2 = 49
We can then take the square root of both sides to solve for t:
t = ±√49
Since we are dealing with time, we discard the negative value. Therefore, the object will take 7 seconds to land on the ground.