Relative motion Transitional Reasoning Download PDF

Questions

1. 1.

   Two autonomous marine research vessels, Alpha and Beta, leave a harbor dock simultaneously on a calm bay. Vessel Alpha cruises at a constant velocity of 25 m/s directed at an angle of $37^\circ$ north of east relative to the water, while Vessel Beta cruises at a constant velocity of 20 m/s due east relative to the water. What is the velocity of Vessel Alpha as observed by an operator aboard Vessel Beta? (Use $\sin 37^\circ = 0.60$ and $\cos 37^\circ = 0.80$.)

   • A) 15 m/s due north
   • B) 15 m/s due south
   • C) 25 m/s due north
   • D) 5 m/s due east
2. 2.

   On two parallel tracks at a railway test facility, an automated cargo train of length 220 m moves due north at a constant speed of 18 m/s relative to the ground. A passenger train of length 180 m travels along the adjacent track, also heading due north at a constant speed of 28 m/s relative to the ground. From the instant the front bumper of the passenger train aligns with the rear bumper of the cargo train, how much time elapses until the rear bumper of the passenger train completely clears the front bumper of the cargo train?

   • A) 40 s
   • B) 22 s
   • C) 18 s
   • D) 4 s
3. 3.

   A student walks due east at a constant speed of 3.0 m/s and observes that raindrops appear to fall purely vertically. When the student increases their speed to run due east at 7.0 m/s, the raindrops appear to strike their umbrella at an angle of $45^\circ$ with the vertical. What is the speed of the raindrops relative to the ground?

   • A) 4.0 m/s
   • B) 5.0 m/s
   • C) 7.6 m/s
   • D) 10.0 m/s
4. 4.

   A river with parallel banks running east-west is 160 m wide and flows steadily due east at a constant speed of 5.0 m/s relative to the riverbanks. An environmental research boat departs from a dock on the south bank, maintaining a constant velocity of 5.0 m/s relative to the water directed at an angle of $53^\circ$ north of west. At what location on the north bank does the boat arrive, measured relative to the point directly across from its launch dock? (Use $\sin 53^\circ = 0.80$ and $\cos 53^\circ = 0.60$.)

   • A) 80 m east of the point directly opposite the launch site
   • B) 200 m east of the point directly opposite the launch site
   • C) 320 m east of the point directly opposite the launch site
   • D) 120 m west of the point directly opposite the launch site
5. 5.

   A delivery drone must travel along a straight path due north relative to the ground between two distribution hubs. A continuous atmospheric wind blows due east at a constant speed of 12 m/s relative to the ground, while the drone maintains a constant speed of 20 m/s relative to the surrounding air. In which direction must the drone be oriented relative to north to maintain its due north ground track, and what is its resulting speed relative to the ground? (Use $\sin 37^\circ = 0.60$ and $\cos 37^\circ = 0.80$.)

   • A) $37^\circ$ east of north, with a ground speed of 16 m/s
   • B) $53^\circ$ west of north, with a ground speed of 12 m/s
   • C) $37^\circ$ east of north, with a ground speed of 23 m/s
   • D) $37^\circ$ west of north, with a ground speed of 16 m/s
6. 6.

   An autonomous oceanographic vessel is heading due north at a constant speed of 15 m/s relative to the water. Its onboard navigation sensor tracks an uncrewed surface craft and reports that the craft is traveling with a velocity of 20 m/s directed due east relative to the vessel. What is the speed and direction of the craft relative to the water?

   • A) 5 m/s directed due east
   • B) 35 m/s directed toward the northeast
   • C) 25 m/s directed toward the southeast
   • D) 25 m/s directed toward the northeast
7. 7.

   A ferry steers across a straight river toward the east bank, maintaining a constant velocity of 4.0 m/s due east relative to the water. The river current flows uniformly due south at 3.0 m/s relative to the riverbank. A jogger on the east bank moves due south along a pathway at a constant speed of 3.0 m/s relative to the ground. What is the velocity of the ferry as measured in the jogger's reference frame?

   • A) 5.0 m/s directed south of east
   • B) 7.2 m/s directed south of east
   • C) 1.0 m/s directed due east
   • D) 4.0 m/s directed due east
8. 8.

   A transport shuttle moves due east along a straight track at a constant speed of 12 m/s relative to the ground. A technician on the shuttle rolls an inspection device forward toward the front of the shuttle at 3 m/s relative to the shuttle floor. Meanwhile, a maintenance cart on an adjacent parallel track travels due west at 8 m/s relative to the ground. What is the velocity of the inspection device as measured by an observer aboard the maintenance cart?

   • A) 7 m/s due east
   • B) 23 m/s due east
   • C) 17 m/s due east
   • D) 23 m/s due west