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?
NNNN noo
To find the time it takes for the object to land on the ground, we need to set the height of the object to zero and solve for time (t).
Given:
h = -16t^2 + s
s = 784 feet (initial height)
h = 0 feet (height when the object lands on the ground)
Substituting the given values into the equation, we have:
0 = -16t^2 + 784
Now, let's solve this quadratic equation for t.
Step 1: Rearrange the equation to isolate t^2.
16t^2 = 784
Step 2: Divide both sides by 16.
t^2 = 49
Step 3: Take the square root of both sides.
t = √49
Since the square root of 49 is 7 (both positive and negative), we have two possible solutions:
t = 7, t = -7
However, time cannot be negative in this context, so we discard the negative value.
Therefore, the object will take 7 seconds to land on the ground.