A helicopter is ascending vertically with a constant speed of 6 meters per second relative to the ground. At the instant the helicopter is 60 meters above the ground it releases a package. What is the magnitude and direction of the velocity of the package, relative to the ground, the instant the package is released by the helicopter?
The Correct Answer and Explanation is :
When the helicopter releases the package, the package’s velocity relative to the ground is the same as the velocity of the helicopter at that instant. The helicopter is ascending vertically with a constant speed of 6 meters per second (m/s), so the package will initially have the same velocity of 6 m/s upwards relative to the ground.
Magnitude and Direction:
- Magnitude: The magnitude of the velocity is 6 m/s.
- Direction: The direction is upwards, since the helicopter is moving upwards at the time of release.
Explanation:
At the moment the package is released, it still has the vertical velocity it shared with the helicopter at that point. This means the package is moving upward at 6 m/s, just as the helicopter was. However, after release, there is no longer any upward force acting on the package (assuming air resistance is negligible). The package is now subject only to gravity, which will start to decelerate it at a rate of 9.8 m/s² (the acceleration due to gravity).
In the first moment after release, the package continues to ascend for a brief period, but it will gradually slow down due to gravity. At some point, its upward velocity will become zero, and then it will start to fall back toward the ground, accelerating downward at 9.8 m/s². This transition from upward motion to downward motion is characteristic of an object in free fall.
However, the question asks for the velocity of the package at the instant of release. Since the package was still moving upwards at that moment with the same speed as the helicopter (6 m/s), the velocity of the package at release is 6 m/s upwards.
Thus, the magnitude of the velocity is 6 m/s, and the direction is upward.