Relative velocity and motion in a plane - One Line Questions

1. 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: — -15i + 20j
2. 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: — -20i - 15j
3. 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: — -4i - 3j
4. 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: — -2i + 6j
5. 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: — -3i - 2j
6. 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: — (4, 6)
7. If v_A = (v_x1, v_y1) and v_B = (v_x2, v_y2), then v_A - v_B is: — (v_x1 - v_x2, v_y1 - v_y2)
8. If a particle's position is described by r(t) = (t^2 - 1)i + (2t + 3)j, its velocity vector at t=0 is: — 0i + 2j
9. 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: — 3 m/s
10. 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: — 10 km/hr South
11. 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: — sqrt(125) m/s
12. 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: — 10i + 15j
13. 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: — 120i + 70j
14. A particle's position is given by r(t) = (t^3 - 3t)i + (2t^2 + 4t)j. Its acceleration vector at t=2 is: — 6i + 4j
15. 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: — 140 km/hr North
16. 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? — 18i + 4j
17. 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: — 200i + 50j
18. 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: — 10i + 20j
19. 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: — 2i
20. 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: — 2i + 2j
21. The velocity vector of a particle is given by v = (2t i + 4j). Its acceleration vector is: — 2i
22. If the position of a particle is given by x = t^2 and y = 2t, its velocity vector is: — 2t i + 2j
23. A particle has velocity v = (3i + 4j) m/s. What is its speed? — 5 m/s
24. A projectile is thrown with velocity v = (3i + 4j) m/s. The horizontal component of velocity is: — 3 m/s
25. 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: — -50i + 300j
26. 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: — 40i - 30j
27. 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: — 4i - 2j
28. 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: — 4i + 3j
29. A particle's position is given by x(t) = 2t^2 and y(t) = 3t. Its velocity vector is: — 4t i + 3j
30. 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
31. 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: — sqrt(125) m/s
32. 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: — 5 m/s upstream
33. 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: — 5i + 5j
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: — 6i - 8j
35. 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: — 0i + 8j km/hr
36. 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: — 70 m/s East
37. 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? — 7i + 3j
38. 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: — 8i - 8j
39. 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? — 4i + 26j
40. A particle moves in the xy-plane with velocity v = (3t^2 - 2t)i + (4t - 1)j. Its acceleration vector at t=2 is: — 8i + 4j
41. 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: — 11i - 3j
42. 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: — i - 4j
43. 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: — -i - j
44. 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: — Two dimensions
45. 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: — sqrt(500) knots
46. 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: — tan(theta) = 4/3
47. 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: — Perpendicular to the river flow
48. A projectile is launched with velocity v_0 at angle theta. The vertical component of its velocity at time t is: — v_0 sin(theta) - gt
49. A particle is projected with velocity v_0 at an angle theta with the horizontal. Its velocity vector in the air is: — v_0 cos(theta) i + (v_0 sin(theta) - gt) j
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: — v_A - v_B
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