2. A drone is flying horizontally at a constant velocity of magnitude at a height above level ground. At time , the drone releases a package. The package falls and lands on the ground at time . Air resistance is negligible. The coordinate system is shown in Figure 1, with the origin at ground level directly below the release point.
Figure 1. Drone releases a package while flying horizontally; coordinate axes and given values.
Figure 2. Blank velocity-component bar charts for the package at two times (ground observer).
Velocity component bar charts can be used to represent the horizontal and vertical components of the package's velocity as measured by an observer on the ground. On the bar charts in Figure 2, draw shaded bars to represent the velocity components and of the package at and at .
Derive an expression for the speed of the package at time as measured by the observer on the ground. Express your answer in terms of , , , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The package is released at and falls to the ground.
Figure 3. Axes for a sketch of vertical position y versus time t until the package reaches the ground.
On the axes in Figure 3, sketch a graph of the vertical position of the package as a function of time from until the package reaches the ground. The graph should be consistent with the given coordinate system and initial conditions. As measured by the observer on the ground, the package follows a parabolic trajectory from release until it hits the ground.
Describe one feature of the package's trajectory as measured by the observer in the drone that differs from the trajectory measured by the observer on the ground. An observer riding in the drone also measures the motion of the package. The drone maintains its constant horizontal velocity of throughout the package's fall.
Briefly justify your answer using principles of relative motion and reference frames.
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