An express train moves due east at 90km⋅h−1 relative to the ground. Inside a passenger car, a student throws a ball horizontally 12m⋅s−1 toward the west relative to the train. At the same instant, a small drone lifts off from the floor and travels 5.0m⋅s−1 due east relative to the train. Neglect vertical motion and treat all velocities as one-dimensional along the east–west track.
Take east as positive.
(a) Convert the train’s speed to m⋅s−1 with appropriate significant figures.
(b) Determine the ball’s velocity (magnitude and direction) relative to the ground.
(c) Determine the drone’s velocity (magnitude and direction) relative to the ground.
(d) Sketch a qualitative velocity–time graph for the ball as seen by the ground observer during the first 2s after the throw, assuming the ball maintains a constant horizontal velocity. Clearly label axes and indicate numerical values where appropriate.