Resolution of a vector, relative velocity, motion in a plane, projectile motion - One Line Questions

1. The time of flight of a projectile launched at an angle θ with initial velocity v is: — (2v sin θ)/g
2. What is the unit vector in the direction of vector A = 3i + 4j? — (3i + 4j)/5
3. The maximum height reached by a projectile launched with initial velocity v at an angle θ with the horizontal is given by: — (v^2 sin^2 θ)/(2g)
4. The range of a projectile launched with initial velocity v at an angle θ with the horizontal is given by: — (v^2 sin(2θ))/g
5. If a projectile is launched vertically upwards with velocity v, the maximum height it reaches is: — (v^2)/(2g)
6. For a given initial speed, the maximum range of a projectile is achieved when the launch angle is: — 45 degrees
7. The angle of projection for maximum range is: — 45°
8. If a projectile is launched with initial velocity v and hits the target at the same horizontal level, the launch angle for maximum height is: — 90°
9. A man walks on a moving walkway. The speed of the man relative to the walkway is 1 m/s, and the speed of the walkway relative to the ground is 2 m/s. If the man walks in the same direction as the walkway, his speed relative to the ground is: — 3 m/s
10. If the man in the previous question walks in the opposite direction to the walkway, his speed relative to the ground is: — 1 m/s
11. A car is moving north at 60 km/h. A truck is moving south at 40 km/h. The relative velocity of the car with respect to the truck is: — 100 km/h North
12. A bird flies with a velocity of 15 m/s in still air. The wind is blowing at 5 m/s due East. If the bird flies in the North direction relative to the ground, its velocity relative to the air must be: — 20 m/s North
13. A plane flies with a speed of 200 km/h relative to the air. The wind is blowing from the west at 50 km/h. To fly due north, the pilot must steer the plane at an angle of approximately: — 15° West of North
14. A vector A has magnitude 5 units and makes an angle of 37 degrees with the positive x-axis. Its x-component is approximately: — 4 units
15. The horizontal range of a projectile is maximum when the angle of projection is: — 45°
16. If a particle is moving in a plane such that its velocity components are v_x = 2 m/s and v_y = 3 m/s, its resultant velocity is: — sqrt(13) m/s
17. A boat is crossing a river. The velocity of the boat relative to the water is 5 m/s and the velocity of the river flow is 2 m/s. If the boat moves perpendicular to the river flow, its resultant velocity with respect to the bank is: — sqrt(29) m/s
18. A vector can be resolved into its components along two non-collinear axes. If a vector A makes an angle θ with the x-axis, its component along the x-axis is given by: — A cos θ
19. If two projectiles are launched with the same initial speed but at complementary angles (e.g., 30° and 60°), their ranges will be: — Same
20. If the resultant velocity of a boat in a river is perpendicular to the river flow, and the velocity of the river is v_r, and the velocity of the boat relative to water is v_b, then v_b must be: — Greater than v_r
21. The maximum height reached by a projectile launched at an angle of 45 degrees is H. What will be the maximum height if the launch angle is 30 degrees with the same initial speed? — 3H/4
22. If a projectile is launched horizontally from a height h, the time taken to reach the ground is the same as the time taken for a body to fall freely from height h. This is because: — Horizontal and vertical motions are independent
23. Two vectors are perpendicular if their dot product is: — Zero
24. Relative velocity is independent of the frame of reference, provided the frames are inertial. This is a consequence of: — Galilean transformations
25. In projectile motion, the trajectory is parabolic because the horizontal motion is uniform (constant velocity) and the vertical motion is uniformly accelerated (due to gravity). This is a consequence of: — Principle of superposition of velocities
26. Motion in a plane involves displacement, velocity, and acceleration vectors that lie in the same plane. This type of motion is also known as: — Two-dimensional motion
27. If a projectile is launched horizontally from a height h with initial velocity u, the time it takes to hit the ground depends on: — Only the height h
28. If a vector is resolved into two perpendicular components, the sum of the squares of the magnitudes of the components is equal to the square of the magnitude of the original vector. This is based on: — Pythagorean theorem
29. If a projectile is launched with speed v at angle θ, and another projectile is launched with speed v at angle (90°-θ), the ratio of their maximum heights will be: — sin^2 θ : cos^2 θ
30. A vector A = 2i - 3j + k. What is the magnitude of A? — sqrt(14)
31. A vector A can be written as A = Ax i + Ay j, where Ax and Ay are its components along the x and y axes respectively. The magnitude of vector A is given by: — sqrt(Ax^2 + Ay^2)
32. The time of flight for a projectile launched horizontally from height h is: — sqrt(2h/g)
33. The path followed by a projectile is a: — Parabola
34. The angle α that vector A = Ax i + Ay j makes with the positive x-axis is given by: — tan α = Ay / Ax
35. A boat moves across a river with velocity 4 m/s relative to the water. The river flows with velocity 3 m/s. If the boat wants to reach the point directly opposite to its starting point, it must aim upstream at an angle θ such that: — tan θ = 3/4
36. For motion in a plane, the velocity vector can be resolved into horizontal and vertical components. If the velocity is v and makes an angle θ with the horizontal, then v_x = v cos θ and v_y = v sin θ. This is true when: — The velocity vector is considered in isolation
37. When two objects A and B are moving in opposite directions with velocities v_A and v_B respectively, their relative velocity of approach is: — v_A + v_B
38. If two objects A and B are moving with velocities v_A and v_B respectively, their relative velocity when moving in the same direction is: — v_A - v_B
39. The relative velocity of object B with respect to object A is given by the formula: — v_B - v_A
40. A projectile is launched with speed v at an angle θ. The velocity at any time t is given by: — v_x = v cos θ, v_y = v sin θ - gt
41. Consider a particle moving in a circle of radius r with constant speed v. Its acceleration is always directed towards the center and its magnitude is: — v^2/r
42. In projectile motion, the quantity that remains constant throughout the flight (neglecting air resistance) is: — Horizontal component of velocity
43. The position of a projectile at any time t, launched with velocity v at angle θ, is given by: — x = (v cos θ) t, y = (v sin θ) t - (1/2)gt^2
44. Two vectors are collinear if they are parallel or anti-parallel. If two vectors are collinear, their cross product is: — Zero
45. In projectile motion, the horizontal component of velocity is: — Constant
46. In projectile motion, neglecting air resistance, the vertical component of acceleration is: — Equal to 'g' downwards
47. If a projectile is launched with velocity v at an angle θ and hits the ground at the same level, its velocity at the highest point is: — v cos θ
48. When a particle moves in a plane with uniform speed, its acceleration is: — Centripetal
49. In projectile motion, the acceleration vector is: — Constant and directed downwards
50. Two vectors are parallel if their cross product is: — Zero
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