Reference Frames And Relative Motion

A helicopter flies due east at 40 m/s relative to the air. The wind blows due south at 30 m/s relative to the ground. Calculate the helicopter’s speed relative to the ground.

A conveyor belt moves at 2.0 m/s to the right relative to the factory floor. A worker places a box on the belt and pushes it to the left at 0.5 m/s relative to the belt. Determine the velocity of the box relative to the factory floor.

Two cyclists ride along a straight road. Cyclist P travels at 12 m/s north and Cyclist Q travels at 8 m/s north, both relative to the ground. Cyclist Q suddenly brakes with an acceleration of 3.0 m/s² southward. What acceleration does Cyclist P measure for Cyclist Q?

A student is solving a relative velocity problem involving a boat crossing a river. The student writes ${\vec{v}}_{BG}={\vec{v}}_{BW}-{\vec{v}}_{WG}$. Which specific error has the student made in applying the subscript chain method?

A physics teacher stands on a moving walkway at an airport that travels at 1.8 m/s east relative to the terminal floor. The teacher throws a ball westward at 3.0 m/s relative to herself. A student standing still in the terminal measures the ball’s velocity. What does the student measure?

An observer on a train platform watches a ball dropped by a passenger on a train moving at constant velocity to the right. The platform observer sees the ball follow a curved (parabolic) path. The train passenger sees the ball fall straight down. Which statement correctly explains this difference?

A rescue boat must reach a point directly across a 200 m wide river. The boat can travel at 6.0 m/s relative to the water, and the river flows at 2.0 m/s eastward relative to the ground. At what angle upstream must the boat aim to arrive directly across, and how long will the crossing take?

A car drives north at 20 m/s on a straight highway. Rain falls vertically at 15 m/s relative to the ground. At what angle from the vertical does the rain appear to strike the car’s windshield, as measured by the driver?

Spaceship Alpha passes a space station at 500 m/s to the right. Spaceship Beta passes the same station at 300 m/s to the left. All velocities are measured relative to the station. Determine the velocity of Spaceship Beta as measured by an observer on Spaceship Alpha.

During a football match, a midfielder runs east at 7 m/s relative to the pitch. She kicks the ball so that a spectator in the stands (at rest relative to the pitch) sees the ball move at 18 m/s due north. Determine the speed and direction of the ball as measured by the midfielder immediately after the kick.

A student argues: “If I measure a car’s velocity as 30 m/s east and you measure it as 10 m/s east, then we must also disagree on the car’s acceleration.” Evaluate this claim. Under what specific condition would the student’s reasoning be correct?

A patrol boat chases a speedboat along a straight canal. The patrol boat moves at 22 m/s east and the speedboat moves at 16 m/s east, both relative to the canal bank. The patrol boat fires a marker dye capsule forward at 10 m/s relative to the patrol boat. Determine the velocity of the dye capsule relative to the speedboat.

A drone hovers stationary relative to the ground. A car passes directly beneath it at 15 m/s east. An observer in the car looks up at the drone. Which description of the drone’s motion, as measured by the car’s observer, is correct?

A swimmer crosses a 120 m wide river. She swims at 2.0 m/s relative to the water, heading straight across (perpendicular to the banks). The river current is 1.5 m/s parallel to the banks. How far downstream from her starting point does she reach the opposite bank?

On a moving train, a child rolls a ball across the aisle (perpendicular to the train’s motion) at 1.0 m/s relative to the train. The train moves at 30 m/s east relative to the ground. A ground observer measures the ball’s velocity. Which statement correctly describes the ground observer’s measurement and why?

A cargo ship sails northeast at 10 m/s relative to the ocean. The ocean current moves the water at 4 m/s due east relative to the seabed. An observer on the seabed wants to determine the ship’s velocity relative to the seabed. Which equation correctly sets up this calculation using the subscript chain method?