Understanding the Vertical Velocity of a Falling Package from a Moving Plane

The motion of a falling package from a moving plane involves considering both its horizontal and vertical components separately. This article focuses on the vertical component of the package's motion, particularly its velocity after 20 seconds.

Initial Considerations

When a plane drops a package, the package has two motions to consider: horizontal and vertical. For the vertical motion, we ignore the horizontal velocity of the plane since the horizontal motion is independent of the vertical motion.

Case Analysis

Let's analyze the given problem in two scenarios where the package is dropped:

Case 1: Zero Initial Vertical Velocity

Here, the package starts from rest in the vertical direction.

Initial Vertical Velocity: 0 m/s Acceleration due to Gravity: 9.81 m/s2 (downward) Time: 20 seconds

Using the equation of motion for vertical motion:

Final velocity initial velocity acceleration x time

Substituting the values:

Final velocity 0 m/s 9.81 m/s2 x 20 s 196.2 m/s (downward)

Therefore, the vertical velocity of the package after 20 seconds is around 196.2 m/s downward.

Case 2: Initial Vertical Velocity of 30 m/s

In this case, the package is dropped with an initial vertical velocity of 30 m/s.

Initial Vertical Velocity: 30 m/s (downward) Acceleration due to Gravity: 9.81 m/s2 (downward) Time: 20 seconds

Using the equation of motion for vertical motion again:

Final velocity initial velocity acceleration x time

Substituting the values:

Final velocity 30 m/s 9.81 m/s2 x 20 s 236.2 m/s (downward)

Therefore, the vertical velocity of the package after 20 seconds is around 236.2 m/s downward.

Practical Considerations for Dropped Packages

It is important to consider the practical feasibility of these scenarios. Dropping a package with an initial vertical velocity of 30 m/s (108 km/h) is extremely high and could result in significant damage. Therefore, the first scenario, where the package is dropped with zero initial vertical velocity, is more practically feasible.

Conclusion

The precise vertical velocity of the package after 20 seconds depends on the scenario and initial conditions. Whether the package is dropped from rest or with an initial vertical velocity, the acceleration due to gravity is the primary factor in determining the final velocity. Proper analysis and consideration of practical factors can help ensure safe and effective package delivery.