Reference Frames and Relative Velocity — Practice Problem Solutions

1. From the passenger's point of view, the ball bounces perfectly normally — straight up and straight back down, just like it would on solid ground. Since the ship cruises at a constant velocity, the passenger and the ball share that same velocity the whole time, so nothing about the bounce looks different from inside that frame.

2. $v_{ground}=1.5+1.0=2.5\text{ m/s}$ (same direction as the walkway).

3. Walking toward the stern is opposite the ship's motion, so $v_{water}=22-2=20\text{ mph}$ (still in the ship's direction of travel, just reduced).

4. The student on the train sees the pencil go straight up and land right back in their hand — a completely ordinary toss, since student and pencil share the train's constant velocity. The platform observer sees the pencil trace a curved (parabolic) path, moving forward with the train the whole time while also rising and falling. Both descriptions are correct — they simply describe the same event from two different reference frames, and velocity (and the resulting path) depends on which frame you're measuring from.

5. $v_{B,rel,A}=v_B-v_A=(-25)-(+30)=-55\text{ m/s}$ — from Train A's perspective, Train B is approaching at 55 m/s.

6. a) Passenger 1: $v_{ground}=2+0=2\text{ m/s}$. Passenger 2: $v_{ground}=2+1.3=3.3\text{ m/s}$. b) Passenger 1 isn't walking, but they're still standing on a walkway that is itself moving relative to the ground — so relative to the ground (not relative to the walkway), they inherit the walkway's own 2 m/s velocity for free.

7. The claim confuses velocity relative to the ground with velocity relative to each other. Since both cars move at 60 mph in the same direction, their relative velocity to each other is $60-60=0\text{ mph}$ — each driver sees the other car sitting motionless alongside them. The 120 mph figure would only be correct if the cars were moving toward each other in opposite directions.

8. (B) — the fly's motion looks completely ordinary to the passenger, exactly as it would in a parked car. A car cruising at constant velocity is an inertial reference frame, so everything inside it (including the fly's buzzing) behaves exactly as it would if the car weren't moving at all.