Motion in a Plane — Previous-Year Questions

Q1. Two forces 3N and 4N act at 90°. Magnitude of resultant:

Q1. Vectors (2,3,1) and (1,−1,2). Dot product:

Q1. î × ĵ equals:

Q1. A projectile is launched at 60° to the horizontal with kinetic energy K. The kinetic energy at the highest point is:

Q2. Two projectiles are thrown with the same speed at angles 45° + α and 45° − α. The ratio of their maximum heights is:

Q3. A ball is projected from the ground at 45° with speed 20 m/s. The radius of curvature at the highest point is (g = 10 m/s²):

Q4. A projectile has the same range R for two angles. If T₁ and T₂ are the times of flight, then R is proportional to:

Q5. A particle is projected at angle θ. If velocity at the highest point is half the velocity of projection, then θ is:

Q6. A projectile reaches max height H. Speed at height H/2 is (launch angle = 60°, initial speed = u):

Q1. Rain falls vertically at 10 m/s. Man walks east at 10 m/s. Umbrella tilt:

Q1. A body moves in a circle of radius 2m at 4 m/s. Centripetal acceleration:

Q1. A boat crosses a 200 m wide river in minimum time of 20 s. Speed of river is 5 m/s. Speed of boat in still water is:

Q2. Two cars A and B move with 60 km/h and 40 km/h in the same direction. Velocity of A relative to B:

Q3. Rain falls vertically at 10 m/s. A man walks at 10 m/s. He should hold umbrella at angle with vertical:

Q4. Two particles start from origin, one with velocity 3î + 4ĵ and other with 5î. Relative velocity magnitude:

Q5. A swimmer crosses a river of width d in time t₁ along shortest path and t₂ along shortest time. If v_s > v_r, then: