⚙️AP Physics C: Mechanics
1. A drone flies horizontally at constant velocity vD = 15.0 m/s in the +x-direction at an altitude h = 45.0 m above level ground. At time t = 0, when the drone is directly above point O on the ground, it releases a package. The package has mass m = 2.0 kg. Air resistance is negligible, and the ground is flat. A coordinate system with origin at point O is shown in Figure 1, where the +x-direction is horizontal and the +y-direction is vertical.
Figure 1
Figure 2
Figure 3
Consider the motion of the package as observed from the ground reference frame.
On the axes in Figure 2, sketch graphs of the x-component of velocity vx and the y-component of velocity vy of the package as functions of time from t = 0 to when the package strikes the ground at t = tf. Clearly label any intercepts, asymptotes, maxima, or minima with numerical values or algebraic expressions, as appropriate.
The position vector of the package as a function of time is given by r⃗(t) = (vD·t)î + (h - (1/2)gt²)ĵ, where g = 10 m/s² and t is measured in seconds.
Derive an expression for the speed v of the package as a function of time. Express your answer in terms of vD, g, h, t, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Draw an arrow on Figure 3 representing the velocity vector of the package at time t = tf as observed from the ground reference frame. The length and direction of the arrow should accurately represent the magnitude and direction of the velocity vector.
In the drone's reference frame, the package appears to follow a different trajectory than it does in the ground reference frame. Describe the shape of the trajectory of the package as observed from the drone's reference frame, and explain your reasoning using principles of relative motion and reference frames. Your explanation should include a comparison to the trajectory observed from the ground reference frame. Now consider the motion of the package as observed from the reference frame of the drone, which continues to move horizontally at constant velocity vD = 15.0 m/s in the +x-direction.
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