The pilot of an airplane traveling 180 km/h wants to drop supplies to flood victims isolated on a patch of land 125 m below. The supplies should be dropped how many seconds before the plane is directly overhead?
______s
How long does it take an object to fall 125m?
125 = .5gt^2
= 5.1s
To determine how many seconds before the plane is directly overhead the supplies should be dropped, we need to calculate the time it takes for the supplies to fall from the plane to the ground.
The key equation we can use for this calculation is the following equation for free fall:
d = (1/2)gt^2
Where:
d = distance traveled (125 m in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
We need to solve this equation for t. Rearranging the equation, we get:
2d = gt^2
Dividing by g on both sides, we have:
2d / g = t^2
Now, let's substitute the known values into the equation:
2(125 m) / 9.8 m/s^2 = t^2
Simplifying the equation, we have:
250 m / 9.8 m/s^2 = t^2
25.51 s^2 = t^2
To find t, we take the square root of both sides:
t = sqrt(25.51 s^2)
Using a calculator, we find:
t ≈ 5.05 s
Therefore, the supplies should be dropped approximately 5.05 seconds before the plane is directly overhead.