Question 1

Car A travels due east at 21 m/s while car B travels due north at 20 m/s. Find the magnitude of the velocity of A relative to B.

Accepted Answer

29 m/s. v_AB = v_A − v_B = (21, 0) − (0, 20) = (21, −20) m/s, so |v_AB| = √(441 + 400) = 29 m/s.

Question 2

To a cyclist riding due east at 12 m/s, a bird appears to fly due north at 35 m/s. Find the true speed of the bird.

Accepted Answer

37 m/s. v_bird = v_cyclist + v_bird/cyclist = (12, 0) + (0, 35) = (12, 35) m/s, so true speed = √(144 + 1225) = 37 m/s.

Question 3

Two particles leave a common point, each moving at 8 m/s, along straight lines 60° apart. Find the magnitude of the velocity of one relative to the other.

Accepted Answer

8 m/s. |v_rel| = 2v sin(θ/2) = 2×8×sin 30° = 8 m/s.

Question 4

Two trains leave a junction at the same moment, each at 7 m/s, along two perpendicular straight tracks. How far apart are they after 10 s?

Accepted Answer

70√2 ≈ 99 m. After 10 s each has gone 70 m along perpendicular directions, so separation = √(70² + 70²) = 70√2 ≈ 99 m.

Question 5

Particle A has velocity (8 î + 4 ĵ) m/s and particle B has velocity (−7 î + 4 ĵ) m/s. Find the speed of A relative to B.

Accepted Answer

15 m/s. v_AB = (8 − (−7), 4 − 4) = (15, 0) m/s, so relative speed = 15 m/s.

Question 6

One drone flies toward the northeast at 10√2 m/s while another flies due north at 10 m/s. Find the speed of the first drone relative to the second.

Accepted Answer

10 m/s. The first drone's velocity is (10, 10) m/s and the second's is (0, 10) m/s, so v_rel = (10, 0) and the relative speed is 10 m/s.

Question 7

Ship A is 85 m due east of ship B. A sails due north at 8 m/s while B sails due east at 15 m/s. Find their distance of closest approach.

Accepted Answer

40 m. Relative to B, A is at (85, 0) m with velocity (−15, 8) m/s (|v_rel| = 17 m/s); closest distance = perpendicular from origin to that line = 85×8/17 = 40 m.

Question 8

Particle A is at the origin moving with velocity (20 î + 10 ĵ) m/s; particle B is at (48 m, 14 m) moving with velocity (−4 î + 3 ĵ) m/s. They collide. Find the time of collision.

Accepted Answer

2 s. v_AB = (24, 7) m/s points exactly along the separation (48, 14) = 2×(24, 7); separation |r| = √(48² + 14²) = 50 m and |v_AB| = 25 m/s, so t = 50/25 = 2 s.

Question 9

A train is 70 m south of a level crossing moving north at 8 m/s; another train is 25 m east of the same crossing moving west at 15 m/s. Find their minimum separation.

Accepted Answer

50 m. Minimum separation = |d₁v₂ − d₂v₁|/√(v₁² + v₂²) = |70×15 − 25×8|/17 = 850/17 = 50 m.

Question 10

Car P is 61 m from an intersection, approaching it at 20 m/s; car Q, on the perpendicular road, is 22 m from it, approaching at 21 m/s. After how much time is their separation minimum?

Accepted Answer

2 s. With D² = (61 − 20t)² + (22 − 21t)², setting dD²/dt = 0 gives 841t = 1682, so t = 2 s (the minimum separation works out to 29 m).

Question 11

An officer stands 80 m due south of a smuggler who runs due east at 12 m/s. The officer runs in a straight line at 20 m/s and just intercepts him. Find the time taken.

Accepted Answer

5 s. To intercept, the officer's east component must be 12 m/s, so his north component is √(20² − 12²) = 16 m/s; t = 80/16 = 5 s.

Question 12

Two shells are fired simultaneously at 20 m/s in the same vertical plane, one at 37° and the other at 53° above the horizontal (sin 37° = 0.6). Find the magnitude of their relative velocity.

Accepted Answer

4√2 ≈ 5.7 m/s. Velocities are (16, 12) and (12, 16) m/s, so v_rel = (4, −4) and |v_rel| = 4√2 ≈ 5.7 m/s; it stays constant since gravity affects both equally.

Question 13

Two motorcyclists start together from a point, each at 20 m/s, along straight roads 60° apart. Find their separation after 6 s.

Accepted Answer

120 m. Relative speed = 2v sin(θ/2) = 2×20×sin 30° = 20 m/s, so separation after 6 s = 20×6 = 120 m.

Question 14

A jeep moves due east at 30 m/s. A drone has true velocity (23 î + 24 ĵ) m/s. Find the drone's speed as it appears to the jeep's driver.

Accepted Answer

25 m/s. v_drone/jeep = (23 − 30, 24 − 0) = (−7, 24) m/s, so apparent speed = √(49 + 576) = 25 m/s.

Question 15

Particle P moves at 40 m/s at 37° above the x-axis (cos 37° = 0.8), while particle Q moves at 32 m/s along the x-axis. Find the speed of P relative to Q.

Accepted Answer

24 m/s. P's velocity is (40×0.8, 40×0.6) = (32, 24) m/s, so v_PQ = (32 − 32, 24) = (0, 24) and the relative speed is 24 m/s.

Question 16

Aircraft A flies due north at 200 m/s. Aircraft B, 2.9 km due north of A, flies due east at 210 m/s at the same altitude. Find their minimum separation.

Accepted Answer

2.1 km. Relative to A, B starts at (0, 2900) m with velocity (210, −200) m/s (|v_rel| = 290 m/s); minimum separation = 2900×210/290 = 2100 m = 2.1 km.

Question 17

A patrol boat 300 m due south of a target ship fires a missile that travels at 40 m/s; the ship sails due east at 24 m/s. At what angle east of north must the missile be aimed to hit the ship?

Accepted Answer

37°. The missile's east component must match the ship: sin α = 24/40 = 0.6, so α = 37° east of north.

Question 18

Two speedboats leave a buoy at the same instant, one due north at 16 m/s and the other due east at 30 m/s. How far apart are they after 5 s?

Accepted Answer

170 m. After 5 s they are at (0, 80) and (150, 0) m, so separation = √(80² + 150²) = 10√(64 + 225) = 170 m.

Question 19

To a driver going due north at 10 m/s, a truck appears to move at 10√2 m/s toward the northeast. Find the truck's true speed.

Accepted Answer

10√5 ≈ 22.4 m/s. v_truck = v_driver + v_apparent = (0, 10) + (10, 10) = (10, 20) m/s, so true speed = √(100 + 400) = 10√5 ≈ 22.4 m/s.

Question 20

Two stones are thrown simultaneously from the same point with velocities (24 î + 30 ĵ) m/s and (10 î + 30 ĵ) m/s. Find their separation 3 s later.

Accepted Answer

42 m. Gravity affects both equally, so their relative velocity is constant: (14, 0) m/s; separation after 3 s = 14×3 = 42 m.

Relative Motion in 2D — JEE Main Physics MCQs with Solutions

Questions with solutions