⚙️AP Physics C: Mechanics
2. A remote-controlled drone moves horizontally at a constant speed of 12 m/s relative to the ground. At time t = 0 s, when the drone is at a height h = 45 m above level ground, it releases a package. The package subsequently moves as a projectile under the influence of gravity alone, as shown in Figure 1. Assume air resistance is negligible and take the acceleration due to gravity to be g = 10 m/s².
Figure 1. Drone releases a package from height 45 m while moving horizontally at 12 m/s (ground frame).
Figure 2. Blank vector diagram for package velocity at t = 1.5 s in Frame G (ground).
On Figure 2, draw a velocity vector to represent the velocity of the package at time t = 1.5 s as observed in Frame G (ground reference frame). The length and direction of your vector should be consistent with the scale indicated, where 1 cm = 5 m/s.
- The vector should originate from the dot representing the package.
- Clearly indicate the magnitude and direction of the velocity vector with appropriate labels.
Derive an expression for the speed of the package at time t = 1.5 s as measured by the observer in Frame D. Express your answer in terms of g, t, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. An observer in Frame D (moving with the drone) also observes the motion of the package after release.
Figure 3. Axes for graphing vertical position y versus time t as observed in Frame D.
On the axes in Figure 3, sketch a graph of the vertical position y of the package as a function of time t as observed in Frame D. Your graph should: The vertical position y of the package as a function of time is now considered from both reference frames.
- Begin at the correct initial position at t = 0 s
- Show the correct curvature
- End at the correct position when the package reaches the ground at t = 3.0 s
Figure 4. Package trajectory in Frame G from release to landing, with positions at t = 0 s, 1.5 s, and 3.0 s.
Describe one feature of the trajectory path shown in Figure 4 (from the first trial) that would be different for the second trial, and state explicitly whether this feature would increase or decrease. In a second trial, the drone moves at a different constant horizontal speed while still at height h = 45 m. The package is released and follows a new trajectory in Frame G, landing at the same time t = 3.0 s but at a different horizontal position than in the first trial.
Justify your answer using physics principles.
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