d = (1/2)g t^2
in feet, seconds units g = 32 ft/s^2 approximately
so
d = 16 t^2
t^2 = d/16
t = (1/4)(sqrt d)
if d = 5280
t = .25 (sqrt 5280)
= .25 * 72.7
=18.2 seconds
To calculate the time it takes for an object to fall a distance d using the formula d = 16t^2, where d is in feet and t is in seconds, you can follow these steps:
1. Convert the given value of d into feet: d = 5280 ft.
2. Plug the value of d into the formula t = (1/4)(√d):
t = (1/4)(√5280)
= (1/4)(72.7)
= 18.2 seconds
Therefore, if d = 5280 ft, the time it takes for the object to fall is approximately 18.2 seconds.
To find the value of t when d = 5280 in the equation d = 16t^2:
1. Substitute the given value of d into the equation:
d = 16t^2
5280 = 16t^2
2. Divide both sides of the equation by 16 to isolate t^2:
t^2 = 5280 / 16
t^2 = 330
3. Take the square root of both sides of the equation to solve for t:
t = √(330)
4. Substitute the approximate value of g, which is 32 ft/s^2, into the equation:
t = (1/4) * √(330)
t ≈ (1/4) * 18.165
5. Simplify to find the final value of t:
t ≈ 4.54125
Therefore, when d = 5280, the value of t is approximately 4.54125 seconds.