"An airplane if flying level at 80.0m above the ground with a speed of 350km/h. The bombardier wishes to drop food and medical supplies to hit a target on the ground. At what horizontal distance from the target should the bombardier release the supplies?"
Calculate the fall time T at that altitude H.
H = g/2 T^2, so
T = sqrt (2H/g)
Assume there is no parachute. At 80 m, a parachute would not open in time anyway.
Multiply the "fall time" by the airplane's speed to get the distance ahead to start the drop.
Sorry, I figured it out!
Oh, thank you drwls!
How long will it take to drop 80 m?
80 = 4.9 t^2
solve for t, the time in the air.
How far will the plane fly in t seconds?
350 km/hr * (1 hr/3600 seconds)* 1000 m/km = 97.2 m/s
distance = speed * time
= 97.2 t
To find the horizontal distance from the target at which the supplies should be released, we need to consider the time it takes for the supplies to reach the target and the horizontal distance covered by the airplane during that time.
First, let's convert the speed of the airplane from km/h to m/s, since the height is given in meters.
350 km/h = (350 * 1000) m/ (60 * 60) s = 97.22 m/s.
Next, let's calculate the time it takes for the supplies to fall from the airplane to the ground. When the supplies are released, they will experience only vertical motion due to gravity, while the airplane simultaneously moves horizontally.
We can calculate the time using the equation:
height = 1/2 * acceleration * time^2.
Since the initial vertical velocity is 0 (objects released from the airplane simply fall), and acceleration due to gravity is approximately 9.8 m/s^2, we can rewrite the equation as:
80 m = 1/2 * 9.8 m/s^2 * time^2.
Simplifying, we get:
time^2 = (2 * 80 m) / 9.8 m/s^2,
time^2 = 16.33 s^2,
time ≈ 4.04 s.
The horizontal distance covered by the airplane in this time can be calculated using the formula:
distance = speed * time.
So the horizontal distance covered by the airplane is:
distance = 97.22 m/s * 4.04 s ≈ 392.6 m.
Therefore, the bombardier should release the supplies approximately 392.6 meters horizontally from the target.