Final answer:
Using the kinematic equation with the given height (305 m) and the acceleration due to gravity, it is calculated that the crate will take approximately 7.88 seconds to fall to the road from a hovering helicopter.
Step-by-step explanation:
To determine how long it takes for the crate to fall to the road from a hovering helicopter at 305 m above the ground, we can use the kinematic equation for constant acceleration, since gravity is the only force acting on the crate (assuming air resistance is negligible).
The formula is:
s = ut + 0.5at^2
Where:
s is the distance the object falls (305 m),
u is the initial velocity (which is 0 m/s, as it falls from rest),
a is the acceleration due to gravity (approximately 9.81 m/s^2),
t is the time in seconds.
Rearranging the formula to solve for t, we get:
t^2 = 2s/a
t = sqrt(2s/a)
Substitute the known values:
t = sqrt(2 * 305 m / 9.81 m/s^2)
t ≈ sqrt(62.07 s^2)
t ≈ 7.88 s
Therefore, it takes the crate approximately 7.88 seconds to reach the road.