A river that flows due east at a steady speed of 1.5\,m/s is 120\,m wide. A small motorboat heads due north across the river at a constant speed of 2.0\,m/s relative to the water. Exactly when the boat reaches the midpoint of the river’s width, a passenger standing on its deck tosses a small rubber ball straight upward with an initial speed of 10\,m/s relative to the deck. The deck is 1.2\,m above the water surface. Neglect air resistance and assume the river current is uniform.
(a) Determine the total time the ball spends in the air before it returns to the deck, as measured by the passenger.
(b) Calculate the ball’s horizontal displacement relative to the shore (east–west and north–south components) from the instant it leaves the passenger’s hand until it lands back on the deck.
(c) Provide parametric equations x(t) and y(t) that describe the ball’s trajectory in the ground (shore) frame, taking the release point as the origin and the east direction as the positive x-axis.
(d) Describe the shape of the ball’s path as viewed by (i) the passenger on the boat and (ii) an observer standing on the shore. Explain, using principles of kinematics, why the two observers see different trajectories even though all observers agree on the ball’s acceleration magnitude and direction.