A rescue airplane is flying horizontally at a height of 3.0 km with a speed 272 m/s when it releases a package of emergency food supplies.

How far horizontally in meters does the package travel while it falls before it hits the ground?

To determine the horizontal distance traveled by the package while falling, we need to calculate the time it takes for the package to hit the ground.

First, let's determine the time it takes for the package to fall from a height of 3.0 km:

Using the equation for free-fall motion:

h = (1/2) * g * t^2

Where:
h = height (3.0 km = 3000 m)
g = acceleration due to gravity (9.8 m/s^2)
t = time

Rearranging the equation:

t^2 = (2h) / g
t^2 = (2 * 3000) / 9.8

Simplifying:

t^2 = 612.24
t = sqrt(612.24)
t ≈ 24.75 seconds

Now that we have the time it takes for the package to fall, we can calculate the horizontal distance traveled by the package using its horizontal velocity:

Distance = Velocity * Time
Distance = 272 m/s * 24.75 s

Calculating the distance:

Distance = 6726 meters

Therefore, the package travels approximately 6726 meters horizontally before it hits the ground.

To find the horizontal distance the package travels while falling, we need to calculate the time it takes for the package to reach the ground.

The time it takes for an object to fall can be found using the equation:

t = sqrt(2h / g)

Where:
t = time (in seconds)
h = height (in meters)
g = acceleration due to gravity (approximately 9.8 m/s²)

Given:
h = 3000 m

Let's substitute the values into the equation to find the time:

t = sqrt(2 * 3000 / 9.8)
= sqrt(6000 / 9.8)
= sqrt(612.24)
≈ 24.74 seconds

So, the package takes approximately 24.74 seconds to reach the ground.

Now we can calculate the horizontal distance traveled using the formula:

d = v * t

Where:
d = distance
v = horizontal velocity (in this case, the same as the airplane's speed, which is 272 m/s)
t = time (in this case, 24.74 seconds)

Let's calculate the distance:

d = 272 * 24.74
≈ 6737.28 meters

Therefore, the package travels approximately 6737.28 meters horizontally before hitting the ground.