AP Physics C Mechanics Quiz: Reference Frames And Relative Motion

Rain is falling vertically downward at a speed of 8 m/s with respect to the ground. A person is riding a bicycle horizontally at a speed of 6 m/s. From the perspective of the cyclist, at what angle from the vertical does the rain appear to fall?

A train moves due east at a constant speed of 20 m/s. A passenger on the train walks toward the front of the train at a speed of 2 m/s relative to the train. What is the velocity of the passenger relative to an observer standing on the ground?

A river flows due south with a speed of 2.0 m/s. A woman in a motorboat wants to travel directly east across the river. The boat's speed relative to the water is 4.0 m/s. At what angle relative to the eastward direction must she point the boat?

A passenger on a cruise ship moving at a constant velocity drops a coin from rest relative to the ship. A stationary observer on a nearby dock watches the coin fall. Which statement best describes the horizontal motion of the coin as seen by the observer on the dock?

Two cars move east on a highway: Car A at $30\ \text{m/s}$ and Car B at $25\ \text{m/s}$. A reference frame is the chosen observer and axes used to measure motion. Relative motion uses velocity differences to describe how one object appears from another. This applies to traffic merging and passing maneuvers. Based on the scenario described, what is the relative speed between the cars?

A train moves east at $20\ \text{m/s}$ while a passenger walks east at $2\ \text{m/s}$ inside. A reference frame is the viewpoint used to measure position and velocity, so motion depends on the chosen frame. Relative motion compares velocities measured in different frames, such as the passenger relative to the train versus the ground. This idea applies to moving vehicles, like commuters walking in buses or luggage carts in airports. Based on the scenario described, what is the velocity of the passenger relative to the train?

Two airplanes fly east: Plane A at $250\ \text{m/s}$ and Plane B at $230\ \text{m/s}$, both relative to the ground. A reference frame is the viewpoint used to measure velocity, such as the ground or one airplane's cockpit. Relative motion compares velocities to find how fast one plane gains on another. This matters for formation flying and air-traffic separation. Based on the scenario described, what is the relative speed of Plane A with respect to Plane B?

A train moves east at $15\ \text{m/s}$ while a passenger walks west at $3\ \text{m/s}$ inside. A reference frame is the coordinate system and observer used to report motion. Relative motion means the same person can have different velocities relative to the train and ground. This appears in real contexts like people walking on moving sidewalks. Based on the scenario described, how does the passenger's motion appear to a stationary observer outside?

An airplane flies east at $200\ \text{m/s}$ relative to the air, while wind blows west at $50\ \text{m/s}$ relative to the ground. A reference frame is the observer's coordinate system, like ground frame versus air frame. Relative motion adds velocity vectors to predict ground speed and direction. This is used for flight planning and drift correction. Based on the scenario described, how does the airplane's motion appear to an observer on the ground?

A river current flows east at $1\ \text{m/s}$ and a rower heads north at $1\ \text{m/s}$ relative to the water. A reference frame is the observer's viewpoint, such as the moving water frame or the stationary riverbank frame. Relative motion combines velocities from different frames to describe what the bank observer sees. This reasoning supports navigation in rivers and air with wind. Based on the scenario described, which frame of reference makes the water appear stationary?

A bus moves east at $12\ \text{m/s}$ while a student walks east at $1\ \text{m/s}$ relative to the bus. A reference frame is the observer's chosen coordinate system for measuring motion. Relative motion means the student's velocity differs when measured from the bus versus the sidewalk. This applies to people moving inside vehicles and conveyor belts. Based on the scenario described, which frame of reference makes the student's speed smallest?

Two cars move in opposite directions: Car A travels east at $20\ \text{m/s}$ and Car B travels west at $15\ \text{m/s}$. A reference frame is the viewpoint used to assign signs and directions to velocities. Relative motion compares one object's velocity as measured from another object's frame. This helps estimate closing speeds in traffic and collision analysis. Based on the scenario described, what is the relative speed between the two cars?

A boat capable of moving at a speed of 5.0 m/s in still water attempts to cross a river that flows due east at 3.0 m/s. The boater points the boat due north. What is the speed of the boat as measured by an observer on the riverbank?

Observer 1 is in a car moving east at a constant velocity of 20 m/s. Observer 2 is in a car moving east at a constant velocity of 30 m/s. Both observers measure the motion of a truck that is accelerating eastward at 2.0 m/s². What are the accelerations of the truck as measured by Observer 1 and Observer 2, respectively?

An airplane has an airspeed of 150 m/s. There is a wind blowing due east at 40 m/s. If the pilot wishes to fly due north relative to the ground, in what approximate direction must the plane be pointed?

A ball is dropped from a helicopter that is moving horizontally at a constant velocity $v_0$. An observer on the ground sees the ball follow a parabolic path. How does the pilot of the helicopter describe the motion of the ball, assuming air resistance is negligible?

The position of particle A is given by the vector function $r_A(t) = (3t^2 - 1)\hat{i} + (4t)\hat{j}$, and the position of particle B is given by $r_B(t) = (2t)\hat{i} + (t^3)\hat{j}$. All quantities are in SI units. What is the velocity of particle A relative to particle B at time $t=2$ s?

An object is accelerating at a rate $a$ relative to the ground. An observer is moving at a constant velocity $v$ relative to the ground. A second observer is accelerating at a rate $a/2$ relative to the ground in the same direction as the object. Which statement correctly describes the acceleration of the object as measured by each observer?

Two observers, Alex on the ground and Ben in a train moving at a constant velocity, both observe a ball being thrown. Which of the following physical quantities must have the same value for both observers?

An observer in a laboratory measures the position of a particle to be $x(t) = At^3$, where A is a positive constant. A second observer is in a reference frame moving with a constant velocity $v_0$ in the positive x-direction relative to the laboratory. What is the acceleration of the particle as measured by the second observer?