Question 1

Ship P sails due east at 9 km/h while ship Q sails due north at 12 km/h. What is the magnitude of the velocity of Q relative to P?

Accepted Answer

15 km/h. v_QP = v_Q − v_P has perpendicular components 12 km/h (north) and 9 km/h (west), so |v_QP| = √(9² + 12²) = 15 km/h.

Question 2

Drone A flies due east at 54 km/h and drone B flies due north at 20 m/s. What is the speed of B relative to A?

Accepted Answer

25 m/s. 54 km/h = 15 m/s; the relative velocity has perpendicular components 15 m/s and 20 m/s, so |v_BA| = √(15² + 20²) = 25 m/s.

Question 3

Trolley A moves due east at 12 m/s and trolley B moves due north at 12 m/s. In which direction does B appear to move as seen from A?

Accepted Answer

45° west of north (towards the north-west). v_BA = v_B − v_A = 12 ĵ − 12 î (m/s): equal components towards the north and the west, which points 45° west of north.

Question 4

Two insects leave the same crumb at the same moment, one crawling east at 0.9 cm/s and the other north at 1.2 cm/s. How far apart are they after 6 s?

Accepted Answer

9 cm. Their separation grows at the relative speed √(0.9² + 1.2²) = 1.5 cm/s, so after 6 s they are 1.5 × 6 = 9 cm apart.

Question 5

Probe A moves due east at 10 m/s and probe B moves due north at 24 m/s. What is the speed of A relative to B?

Accepted Answer

26 m/s. The velocities are perpendicular, so |v_AB| = √(10² + 24²) = √676 = 26 m/s.

Question 6

Robot A has velocity 7 î + 2 ĵ (m/s) and robot B has velocity −2 î − 10 ĵ (m/s). What is the speed of A relative to B?

Accepted Answer

15 m/s. v_AB = v_A − v_B = (7 − (−2), 2 − (−10)) = (9, 12) m/s, so |v_AB| = √(81 + 144) = 15 m/s.

Question 7

Two spheres are rolled from the same corner of a hall at the same moment, one east at 2.1 m/s and the other north at 2.8 m/s. How far apart are they after 10 s?

Accepted Answer

35 m. Relative speed = √(2.1² + 2.8²) = 3.5 m/s, so separation after 10 s = 3.5 × 10 = 35 m.

Question 8

Two ships leave the same port together, one heading due east at 16 km/h and the other due north at 30 km/h. How far apart are they after 30 minutes?

Accepted Answer

17 km. Relative speed = √(16² + 30²) = 34 km/h; in 0.5 h the separation is 34 × 0.5 = 17 km.

Question 9

Two drones take off from the same helipad at the same moment, each flying at 20 m/s, with their directions 60° apart. How far apart are they after 4 s?

Accepted Answer

80 m. For equal speeds v at angle θ, |v_rel| = 2v sin(θ/2) = 2 × 20 × sin 30° = 20 m/s; separation = 20 × 4 = 80 m.

Question 10

Two ships leave the same port at the same time, one due east at 21 km/h and the other due north at 28 km/h. After how much time are they 70 km apart?

Accepted Answer

2 h. The separation grows at √(21² + 28²) = 35 km/h, so t = 70 / 35 = 2 h.

Question 11

Trolley A is 60 m west of a junction moving east at 12 m/s, and trolley B is 45 m south of the same junction moving north at 9 m/s. How far apart are they 2 s later?

Accepted Answer

45 m. At t = 2 s, A is 60 − 24 = 36 m west and B is 45 − 18 = 27 m south of the junction; separation = √(36² + 27²) = √2025 = 45 m.

Question 12

Drone B is 65 m due north of drone A. A flies due east at 24 m/s and B flies due south at 10 m/s. What is the minimum distance between them? (Both fly at the same height.)

Accepted Answer

60 m. Relative to A, B moves with velocity (−24, −10) m/s, |v_rel| = 26 m/s; the closest approach is the perpendicular distance 65 × (24/26) = 60 m.

Question 13

Probe B is 125 m due north of probe A. A moves due east at 20 m/s and B moves due south at 15 m/s. After how much time is the separation between them minimum?

Accepted Answer

3 s. Relative to A, B has velocity (−20, −15) m/s with |v_rel| = 25 m/s; time of closest approach = (125 × 15)/25² = 1875/625 = 3 s.

Question 14

An observer on trolley A, moving due east at 21 m/s, sees ball B moving due north at 28 m/s. What is the true speed of B relative to the ground?

Accepted Answer

35 m/s. v_B = v_A + v_BA = (21, 0) + (0, 28) = (21, 28) m/s, so the true speed is √(441 + 784) = 35 m/s.

Question 15

Sphere A rolls due north at 14 m/s and sphere B rolls due east at 14 m/s. What is the magnitude of the velocity of B relative to A?

Accepted Answer

14√2 ≈ 19.8 m/s. v_BA = (14, −14) m/s (east and south components), so |v_BA| = 14√2 ≈ 19.8 m/s.

Question 16

Robot A is 80 m west of a crossing, moving east at 10 m/s. Robot B is 96 m south of the crossing and starts at the same moment. At what speed must B move north so that both reach the crossing together?

Accepted Answer

12 m/s. A reaches the crossing in 80/10 = 8 s, so B needs 96/8 = 12 m/s.

Question 17

Two insects leave the same grain at the same moment, each crawling at 2.4 cm/s, with their paths 60° apart. How far apart are they after 5 s?

Accepted Answer

12 cm. |v_rel| = 2v sin(θ/2) = 2 × 2.4 × sin 30° = 2.4 cm/s, so separation = 2.4 × 5 = 12 cm.

Question 18

Drone A is 46 m east of a checkpoint, flying west at 10 m/s; drone B is 60 m north of the checkpoint, flying south at 10 m/s. How far apart are the drones 3 s later?

Accepted Answer

34 m. At t = 3 s, A is 46 − 30 = 16 m east and B is 60 − 30 = 30 m north of the checkpoint; separation = √(16² + 30²) = 34 m.

Question 19

Probe A has velocity 10 î − 6 ĵ (m/s) and probe B has velocity −8 î + 12 ĵ (m/s). What is the speed of A relative to B?

Accepted Answer

18√2 ≈ 25.5 m/s. v_AB = (10 − (−8), −6 − 12) = (18, −18) m/s, so |v_AB| = 18√2 ≈ 25.5 m/s.

Question 20

Ball A is 45 m west of a corner mark, rolling east at 9 m/s. Ball B starts from the mark at the same moment, rolling north at 12 m/s. How far apart are the balls 3 s later?

Accepted Answer

18√5 ≈ 40.2 m. At t = 3 s, A is 45 − 27 = 18 m west of the mark and B is 36 m north of it; separation = √(18² + 36²) = √1620 = 18√5 ≈ 40.2 m.

Relative Motion in 2D — IISER Physics MCQs with Solutions

Questions with solutions