Relative velocity in two dimensions Knowledge-Based Download PDF

Questions

1. 1.

   A straight river of width 200 m flows due east with a uniform current of 4.0 m/s relative to the riverbank. A boat sets out from the south bank with a speed of 10 m/s relative to the water, steered at an angle of 30° north of east. How much time does the boat take to reach the opposite bank?

   • A) 20 s
   • B) 25 s
   • C) 50 s
   • D) 40 s
2. 2.

   Sailboat Alpha sails due east at a constant speed of 6.0 m/s relative to the water, while Sailboat Beta sails due north at the same constant speed of 6.0 m/s relative to the water. What is the direction of the velocity of Sailboat Beta relative to Sailboat Alpha?

   • A) 45° north of east
   • B) 45° south of east
   • C) 45° north of west
   • D) 45° south of west
3. 3.

   A patrol boat moves due north at a constant speed of 20 m/s relative to the water. An aerial drone moves such that its velocity relative to the patrol boat is $20\sqrt{2}\text{ m/s}$ directed 45° south of east. What is the speed of the drone relative to the water?

   • A) 40 m/s
   • B) $20\sqrt{3}\text{ m/s}$
   • C) $20\sqrt{2}\text{ m/s}$
   • D) 20 m/s
4. 4.

   A cruise ship sails due north at a constant speed of 4.0 m/s relative to the water, while a passenger walks directly across the deck from west to east at a constant speed of 3.0 m/s relative to the ship. What is the magnitude of the passenger's displacement relative to the water during an interval of 10 seconds?

   • A) 70 m
   • B) 40 m
   • C) 50 m
   • D) 30 m
5. 5.

   Ship X travels due east at a constant speed of 30 km/h relative to the water, while Ship Y travels at 30 km/h in a direction 60° north of east relative to the water. What is the magnitude of the velocity of Ship Y relative to Ship X?

   • A) 0 km/h
   • B) 15 km/h
   • C) 30 km/h
   • D) 60 km/h
6. 6.

   A research vessel sails due west at a constant speed of 12 km/h relative to the water, while an onboard sensor records the wind blowing due north relative to the vessel at 16 km/h. What is the speed of the wind relative to the water?

   • A) 4 km/h
   • B) 14 km/h
   • C) 20 km/h
   • D) 28 km/h
7. 7.

   A motorboat is steered directly across a straight river of width 160 m at a constant speed of 4.0 m/s relative to the water. If the river current flows downstream at 3.0 m/s relative to the bank, what is the boat's downstream drift distance upon reaching the opposite bank?

   • A) 40 m
   • B) 160 m
   • C) 120 m
   • D) 200 m
8. 8.

   A train travels due east at 15 m/s relative to the ground, while a passenger on the train observes a drone flying due north at 8 m/s relative to the train. What is the speed of the drone relative to the ground?

   • A) 17 m/s
   • B) 23 m/s
   • C) 7 m/s
   • D) 13 m/s
9. 9.

   An airplane has an airspeed of 100 km/h relative to the air and encounters a uniform wind blowing due east at 50 km/h relative to the ground. In which direction must the pilot head the aircraft so that its resultant motion is directed due north relative to the ground?

   • A) 60° west of north
   • B) 30° west of north
   • C) 30° east of north
   • D) 45° west of north
10. 10.

    Rain falls vertically downward at a constant speed of 12 m/s relative to the ground. A runner travels along a straight, horizontal path due north at 12 m/s relative to the ground. At what angle relative to the vertical does the rain appear to fall to the runner?

    • A) 30° toward the north
    • B) 45° toward the south
    • C) 45° toward the north
    • D) 60° toward the south
11. 11.

    Two particles, P and Q, move in the xy-plane with constant velocities relative to the ground given by $\vec{v}_{\text{P}} = (2\hat{i} + 5\hat{j})\text{ m/s}$ and $\vec{v}_{\text{Q}} = (-2\hat{i} + 2\hat{j})\text{ m/s}$. What is the magnitude of the velocity of particle P relative to particle Q?

    • A) 3 m/s
    • B) 4 m/s
    • C) 5 m/s
    • D) 7 m/s
12. 12.

    A swimmer capable of swimming at 1.5 m/s relative to the water crosses a river flowing at 0.9 m/s relative to the riverbank. If the swimmer steers so that their resultant motion relative to the riverbank is directly perpendicular to the current, what is the swimmer's speed relative to the riverbank?

    • A) 0.6 m/s
    • B) 1.2 m/s
    • C) 1.7 m/s
    • D) 2.4 m/s
13. 13.

    Car A moves due north at 12 m/s relative to the ground, while Car B moves due east at 16 m/s relative to the ground. What is the magnitude of the velocity of Car A relative to Car B?

    • A) 4 m/s
    • B) 14 m/s
    • C) 28 m/s
    • D) 20 m/s