Relative velocity and motion in a plane - Question Bank
1. Two particles P and Q are moving with velocities v_P = (4i + 3j) m/s and v_Q = (2i + j) m/s. The relative velocity of P with respect to Q is:
2. A swimmer can swim at 6 m/s in still water. He wants to cross a river of width 120 m flowing at 8 m/s. To cross the river in the shortest possible time, he should swim:
3. The velocity vector of a particle is given by v = (2t i + 4j). Its acceleration vector is:
4. A ship is moving at 20 knots due east. A current flows north at 10 knots. The resultant velocity of the ship relative to the seabed is:
5. A particle moves in the xy-plane. Its velocity components are v_x = 2t and v_y = 3. If its initial position is (0,0), its position at t=2 is:
6. If the velocity of rain is v_r = (-3i - 4j) km/hr and a cyclist is moving with v_c = (i - j) km/hr, the velocity of rain relative to the cyclist is:
7. A projectile is thrown with velocity v = (3i + 4j) m/s. The horizontal component of velocity is:
8. A boat heads upstream at 10 m/s. The river flows downstream at 5 m/s. The velocity of the boat relative to the bank is:
9. A particle's position is given by r(t) = (t^3 - 3t)i + (2t^2 + 4t)j. Its acceleration vector at t=2 is:
10. Two particles A and B are moving in the xy-plane with velocities v_A = (3i - 2j) m/s and v_B = (i + 4j) m/s. The relative velocity of B with respect to A is:
11. A plane's airspeed is 300 km/hr. It is flying due north. The wind is blowing from the west at 50 km/hr. The velocity of the plane relative to the ground is:
12. If the position of a particle is given by x = t^2 and y = 2t, its velocity vector is:
13. A person walks east at 4 km/hr. The river flows north at 3 km/hr. The velocity of the person relative to the river bank is:
14. The position of a particle is given by r(t) = (5t i + 10t^2 j). The magnitude of its velocity at t=1 is:
15. Two particles A and B have velocities v_A = (2i + 3j) m/s and v_B = (i + 2j) m/s. The relative velocity v_B - v_A is:
16. A boat travels north at 30 km/hr. A wind blows southwest at 40 km/hr. The velocity of the boat relative to the ground is approximately:
17. A projectile is launched with velocity v_0 at angle theta. The vertical component of its velocity at time t is:
18. A particle moves in the xy-plane with velocity v = (3t^2 - 2t)i + (4t - 1)j. Its acceleration vector at t=2 is:
19. The velocity of a car is v_c = (10i + 20j) m/s. The velocity of a motorcycle is v_m = (5i + 15j) m/s. The velocity of the car relative to the motorcycle is:
20. A swimmer can swim at 5 m/s in still water. He swims across a river of width 100m flowing at 10 m/s. If he swims perpendicular to the flow, his resultant velocity relative to the bank is:
21. A particle's position is given by x(t) = 2t^2 and y(t) = 3t. Its velocity vector is:
22. If the velocity of a particle is given by v = (3i + 4j) m/s, its direction of motion with respect to the positive x-axis is given by an angle theta such that:
23. A boat is steered due west at 15 km/hr in a river flowing north at 20 km/hr. The velocity of the boat relative to the river bank is:
24. Two trains A and B are moving on parallel tracks. Train A moves east at 30 m/s. Train B moves west at 40 m/s. The velocity of train A relative to train B is:
25. A plane flies north at 200 km/hr. The wind blows east at 50 km/hr. The velocity of the plane relative to the air is:
26. The position vector of a particle is r(t) = (t^2 i + t j). Its velocity vector is v(t) = 2t i + j. The acceleration vector is:
27. A particle has velocity v = (3i + 4j) m/s. What is its speed?
28. A boat can move at 10 m/s in still water. It wants to cross a river flowing at 5 m/s. If the boat heads perpendicular to the river flow, its velocity relative to the bank will be:
29. If a particle's position is described by r(t) = (t^2 - 1)i + (2t + 3)j, its velocity vector at t=0 is:
30. Two cars A and B are moving on a straight road. Car A moves north at 60 km/hr. Car B moves south at 80 km/hr. The velocity of car A relative to car B is:
31. A person walks on a moving walkway. The person walks at 2 m/s relative to the walkway, and the walkway moves at 1 m/s relative to the ground. If the person walks in the same direction as the walkway, their speed relative to the ground is:
32. The velocity of a particle is given by v(t) = (2t i + 3t^2 j). What is its displacement from t=1 to t=3?
33. A cyclist is moving north at 15 m/s. A car is moving west at 20 m/s. The velocity of the car relative to the cyclist is:
34. A ship is moving with velocity (4i - 3j) km/hr. A submarine is moving with velocity (-2i + 5j) km/hr. The velocity of the ship relative to the submarine is:
35. A particle's position is given by r(t) = t^3 i + (2t^2 - 5t) j. What is its acceleration vector at t = 3 seconds?
36. If v_A = (v_x1, v_y1) and v_B = (v_x2, v_y2), then v_A - v_B is:
37. A bird flies with velocity (5i - 12j) km/hr. It is flying in a wind blowing with velocity (3i + 4j) km/hr. The velocity of the bird relative to the ground is:
38. A projectile is fired with initial velocity u at an angle alpha to the horizontal. The horizontal component of its velocity remains constant, while the vertical component changes due to gravity. This describes motion in:
39. Two particles P and Q are moving with velocities v_P = (2i - j) m/s and v_Q = (i + 3j) m/s. The velocity of P relative to Q is:
40. A boat heads due north at 20 m/s in a river flowing east at 10 m/s. The velocity of the boat relative to the bank is:
41. The acceleration of a particle moving in a plane is given by a = (2i + 3j) m/s^2. If its initial velocity is zero, its velocity at t = 5 seconds will be:
42. A car moves north at 30 m/s. Another car moves east at 40 m/s. The velocity of the second car relative to the first car is:
43. The position of a particle is given by x(t) = 5t^3 - 2t^2 + 4, y(t) = 3t^2 - 6t + 1. The velocity vector at t=1 is:
44. A plane is flying with velocity (100i + 20j) km/hr. A wind blows with velocity (20i + 50j) km/hr. The velocity of the plane relative to the ground is:
45. Two particles A and B are moving in the xy-plane. Particle A has velocity v_A = (3i + 2j) m/s and particle B has velocity v_B = (-i + 4j) m/s. The relative velocity of A with respect to B is:
46. A particle is projected with velocity v_0 at an angle theta with the horizontal. Its velocity vector in the air is:
47. If the velocity of rain is v_r = (-2i - 3j) km/hr and the velocity of a man walking is v_m = (i - j) km/hr, the velocity of rain relative to the man is:
48. A particle moves in the xy-plane such that its position vector is given by r(t) = (2t^2 - t)i + (3t - 5)j. What is its velocity vector at t = 2 seconds?
49. A boat is moving with velocity (3i + 4j) km/hr in a river. The river is flowing with velocity (-3i + 4j) km/hr. The velocity of the boat relative to the river bank is:
50. Two bodies A and B move with velocities v_A and v_B respectively. The relative velocity of A with respect to B is given by: