Answer:
d = 256 ft.
Step-by-step explanation:
The distance an object falls is directly proportional to the square of the time it falls.
First, we name the variables.
Let d= the distance.
t= time
Write the formula for direct variation, where y varies directly with the square of x.
y=kx2
We will use d in place of y and t in place of x.
d=kt2
Substitute the given values for the variables.
d=144whent=3144=k⋅32
Solve for the constant of variation.
144916=k⋅99=k
Write the equation that relates d and t.
d=kt2
Substitute in the constant of variation.
d=16t2
Find d when t=4.
Write the equation that relates d and t.
d=16t2
Substitute the given value for t.
d=16⋅42
Simplify.
d=256
An object will fall 256 feet in 4 seconds.
