Frames of reference Transitional Reasoning Practice

Questions

1. 1.

   Two autonomous survey rovers, Rover Alpha and Rover Beta, travel across a flat open test field. Rover Alpha moves due north at a constant speed of 3.0 m/s relative to the ground, while Rover Beta moves due east at a constant speed of 4.0 m/s relative to the ground. An engineer uses an onboard tracking sensor mounted on Rover Alpha to observe the motion of Rover Beta. In the frame of reference of Rover Alpha, what are the magnitude and direction of Rover Beta's velocity?

   • A) 1.0 m/s directed due east
   • B) 5.0 m/s directed northeast
   • C) 5.0 m/s directed southeast
   • D) 7.0 m/s directed southeast
2. 2.

   Two research capsules, Capsule 1 and Capsule 2, are released from rest from the top of an evacuated vertical drop tower. Capsule 2 is released exactly 1.0 second after Capsule 1, and both capsules fall freely under gravity with the same constant downward acceleration $g$ relative to the ground. An onboard tracking sensor in Capsule 2 records the motion of Capsule 1 during their descent. Which statement correctly describes the acceleration and velocity of Capsule 1 in the frame of reference of Capsule 2?

   • A) Capsule 1 remains at a fixed distance with zero relative velocity and zero acceleration because both capsules experience the same gravitational acceleration.
   • B) Capsule 1 accelerates downward at $g$ with a continuously increasing speed because gravity acts continuously on both falling capsules.
   • C) Capsule 1 accelerates downward with an increasing relative speed because its instantaneous speed relative to the ground is always greater than that of Capsule 2.
   • D) Capsule 1 moves downward at a constant speed with zero acceleration because both capsules have identical downward accelerations relative to the ground.
3. 3.

   A remote-controlled test car accelerates uniformly from 4 m/s to 12 m/s along a straight track in 4.0 seconds, as recorded by a stationary sensor on the ground. Simultaneously, a tracking drone flies parallel to the track at a constant velocity of 4 m/s in the same direction. How do the test car's measured acceleration and displacement during this 4.0-second interval compare between the ground frame of reference and the drone's frame of reference?

   • A) The measured acceleration is greater in the ground frame of reference, while the displacement is the same in both frames.
   • B) Both the measured acceleration and the displacement are the same in both frames of reference.
   • C) The measured acceleration is the same in both frames of reference, while the displacement is smaller in the drone's frame.
   • D) Both the measured acceleration and the displacement are smaller in the drone's frame of reference.
4. 4.

   Two navigational beacons, Beacon 1 and Beacon 2, are anchored to the seabed and remain stationary 120 meters apart along an east-west shipping channel. A patrol boat travels due east along the straight line from Beacon 1 toward Beacon 2 at a constant velocity of 6 m/s relative to the seabed. A researcher on board the boat analyzes the motion of both beacons using the boat as the reference frame. Which statement correctly describes the velocities of the beacons and the distance between them in the patrol boat's frame of reference?

   • A) Both beacons have a velocity of 6 m/s due east, and the distance between the beacons decreases over time.
   • B) Both beacons have a velocity of 6 m/s due west, and the distance between the beacons remains constant at 120 meters.
   • C) Beacon 1 has a velocity of 6 m/s due west while Beacon 2 has a velocity of 6 m/s due east, and the distance between the beacons decreases over time.
   • D) Beacon 1 is stationary while Beacon 2 has a velocity of 6 m/s due west, and the distance between the beacons decreases over time.
5. 5.

   In a fulfillment facility, an automated scanner travels due east along an overhead rail at a constant velocity of 5.0 m/s relative to the warehouse floor. Directly below it, a package rides on a horizontal conveyor belt moving due east at a constant velocity of 2.0 m/s relative to the floor, while a technician stands stationary on the floor. Which statement correctly describes the velocities of the package and the technician as measured from the frame of reference of the moving scanner?

   • A) The package moves at 7.0 m/s east, and the technician moves at 5.0 m/s east.
   • B) The package moves at 3.0 m/s east, and the technician remains at rest.
   • C) The package moves at 3.0 m/s west, and the technician remains at rest.
   • D) The package moves at 3.0 m/s west, and the technician moves at 5.0 m/s west.
6. 6.

   On a windless day, raindrops fall vertically downward at a constant velocity relative to the ground. A runner jogs along a straight horizontal path due east at a constant speed. To minimize getting wet, in which direction must the runner tilt the top of the umbrella relative to the vertical, and why?

   • A) The runner should hold the umbrella vertically upright, because the motion of an observer does not alter the direction of falling rain in any frame of reference.
   • B) The runner should tilt the top of the umbrella toward the west, because the runner's eastward motion causes the rain to appear to travel toward the east in the runner's frame of reference.
   • C) The runner should hold the umbrella vertically upright, because both the runner and the raindrops are moving within the same Earth-fixed frame of reference.
   • D) The runner should tilt the top of the umbrella toward the east, because in the runner's frame of reference, the raindrops possess an apparent westward horizontal velocity component.
7. 7.

   Two autonomous delivery rovers, Rover X and Rover Y, move side by side along a straight horizontal path at the same constant velocity of 2 m/s due east relative to the ground. A technician stands at a stationary test station beside the path, while an onboard sensor on Rover X continuously tracks the motion of Rover Y. Over a time interval of 10 seconds, how do the observed motion and distance traveled by Rover Y compare between the technician's frame of reference and Rover X's frame of reference?

   • A) In the technician's reference frame, Rover Y is stationary and covers 0 m, while in Rover X's reference frame, it travels east and covers 20 m.
   • B) Both reference frames measure Rover Y traveling a distance of 20 m because distance is an absolute quantity independent of any observer.
   • C) In the technician's reference frame, Rover Y travels east and covers 20 m, whereas in Rover X's reference frame, Rover Y remains stationary and covers 0 m.
   • D) In the technician's reference frame, Rover Y covers 20 m, while in Rover X's reference frame, Rover Y moves west and covers 40 m due to relative motion.
8. 8.

   A motorized cart moves along a straight horizontal track at a constant velocity. A vertical launcher mounted on the cart projects a small sphere straight upward into the air, which later lands precisely back in the launcher. Student 1 is seated on the cart moving with it, while Student 2 stands stationary beside the track on the laboratory floor. Neglecting air resistance, which statement correctly compares the trajectory of the sphere as observed by Student 1 and Student 2?

   • A) Both observers see the sphere follow an identical parabolic path because gravitational acceleration is the same in all reference frames.
   • B) Student 1 observes the sphere follow a curved parabolic path, whereas Student 2 observes it move strictly along a vertical straight line.
   • C) Student 1 observes the sphere move strictly along a vertical straight line, whereas Student 2 observes it follow a curved parabolic path.
   • D) Both observers see the sphere move strictly along a vertical straight line because the launcher exerts a force only in the vertical direction.
9. 9.

   A passenger train travels along a straight track at a constant velocity of 15 m/s due north relative to the ground. Inside the train, a passenger rolls a ball along the aisle at a constant speed of 3 m/s due south relative to the floor of the train. An observer stands stationary on the platform observing the train pass. Which statement correctly describes the velocity of the ball in the train's frame of reference compared to the platform observer's frame of reference?

   • A) In the train's frame of reference, the ball moves south at 12 m/s, while in the platform observer's frame of reference, it moves south at 3 m/s.
   • B) In the train's frame of reference, the ball moves north at 3 m/s, while in the platform observer's frame of reference, it moves north at 18 m/s.
   • C) In the train's frame of reference, the ball moves south at 3 m/s, while in the platform observer's frame of reference, it moves north at 12 m/s.
   • D) In both frames of reference, the ball moves south at 3 m/s because an object's velocity is absolute and independent of the observer.

Answers and step-by-step solutions appear after you finish the test.