NARAYANA CO PROGRAM 9TH CLASS PHYSICS COREQUEST
WEEK-12
PHYSICS 29-08-2026
TOPIC: RELATIVE MOTION - 2D
Sub-Topics Covered:
• Rate of approach and rate of separation | Closest approach
• Condition for collision of bodies in 2D and 3D
• Relative motion of one projectile with respect to another projectile
• Condition for collision of two projectiles
• Projectiles launched from moving platforms and real-world applications
SECTION A: MODERATE LEVEL QUESTIONS (Q.1 to Q.10)
Q1. Two particles A and B are moving in the x-y plane with velocities v _A = (3î + 4ĵ) m/s and v _B = (-î + 7ĵ)
m/s respectively. What is the magnitude of the relative velocity of particle B with respect to particle A?
(A) 5 m/s (B) 7 m/s
(C) 25 m/s (D) 1 m/s
Q2. Particle A is at position r _A = (2î + 3ĵ) m and particle B is at r _B = (10î + 9ĵ) m. If velocity of A is v _A =
2î m/s and velocity of B is v _B = -2î m/s, at what rate is the distance between them changing initially?
(A) -4.0 m/s (B) -3.2 m/s
(C) -2.5 m/s (D) -1.8 m/s
Q3. Two projectiles 1 and 2 are launched simultaneously from the ground with initial speeds u₁ = 20 m/s at
θ₁ = 30° and u₂ = 20 m/s at θ₂ = 60° above horizontal in the same direction. What is the path (trajectory)
of projectile 2 as seen by projectile 1 during their time in flight?
(A) Parabola (B) Straight line angled to horizontal
(C) Vertical straight line (D) Circle
Q4. Particle A moves with constant velocity vA = 10î m/s from origin (0,0). Particle B moves with constant
velocity vB = -10ĵ m/s from initial position (0, 100 m). What is the minimum distance (distance of closest
approach) between them?
(A) 50 m (B) 50√2 m
(C) 100 m (D) 25√2 m
Q5. A platform is moving horizontally with a constant velocity of 5 m/s. A projectile is launched from this
platform with a velocity of 20 m/s relative to the platform at an angle of 30° to the platform. What is the
total horizontal velocity component of the projectile relative to the ground?
9TH-CO IIT_PHYSICS 1|Pa ge
, NARAYANA CO PROGRAM 9TH CLASS PHYSICS COREQUEST
(A) 10√3 m/s (B) (10√3 + 5) m/s
(C) (10 + 5√3) m/s (D) 15 m/s
Q6. Two bodies are projected simultaneously from the same point in space with speeds u₁ = 10 m/s and u₂ =
10 m/s in directions making angles 30° and 60° with the horizontal respectively. Find the distance
between them after t = 1 s. (g = 10 m/s²)
(A) 10(√3 - 1) m (B) 10√(2 - √3) m
(C) 10 m (D) 5√2 m
Q7. A ship A is moving westwards at a speed of 10 km/h and a ship B 100 km south of A is moving
northwards at 10 km/h. How long will they take to reach the distance of closest approach?
(A) 2.5 hours (B) 5.0 hours
(C) 7.07 hours (D) 10.0 hours
Q8. For two projectiles projected from two different points in the same vertical plane to collide in mid-air,
which of the following conditions MUST be satisfied?
(A) Their horizontal components of velocity (B) Their vertical components of relative
must be equal. velocity must be zero at all times.
(C) The relative velocity vector must be initially (D) Their ranges must be equal.
irected along the line joining the two points.
Q9. A cart moves horizontally with a constant acceleration a₀ = 2 m/s². A ball is thrown vertically upward
relative to the cart with speed 10 m/s from the cart floor. What is the horizontal distance between the
ball and the launch point on the cart when the ball returns to the cart floor? (g = 10 m/s²)
(A) 2 m (B) 4 m
(C) 0 m (D) 8 m
Q10. Two particles A and B move with constant speeds v₁ and v₂ along two mutually perpendicular straight
paths intersecting at O. At t = 0, they are at distances x₁ and x₂ from O and moving towards O. The time
when they are closest to each other is:
(A) (x₁v₁ + x₂v₂) / (v₁² + v₂²) (B) (x₁v₂ + x₂v₁) / (v₁² + v₂²)
(C) (x₁v₁ - x₂v₂) / (v₁² + v₂²) (D) √(x₁² + x₂²) / √(v₁² + v₂²)
SECTION B: DIFFICULT LEVEL QUESTIONS (Q.11 to Q.20)
9TH-CO IIT_PHYSICS 2|Pa ge
WEEK-12
PHYSICS 29-08-2026
TOPIC: RELATIVE MOTION - 2D
Sub-Topics Covered:
• Rate of approach and rate of separation | Closest approach
• Condition for collision of bodies in 2D and 3D
• Relative motion of one projectile with respect to another projectile
• Condition for collision of two projectiles
• Projectiles launched from moving platforms and real-world applications
SECTION A: MODERATE LEVEL QUESTIONS (Q.1 to Q.10)
Q1. Two particles A and B are moving in the x-y plane with velocities v _A = (3î + 4ĵ) m/s and v _B = (-î + 7ĵ)
m/s respectively. What is the magnitude of the relative velocity of particle B with respect to particle A?
(A) 5 m/s (B) 7 m/s
(C) 25 m/s (D) 1 m/s
Q2. Particle A is at position r _A = (2î + 3ĵ) m and particle B is at r _B = (10î + 9ĵ) m. If velocity of A is v _A =
2î m/s and velocity of B is v _B = -2î m/s, at what rate is the distance between them changing initially?
(A) -4.0 m/s (B) -3.2 m/s
(C) -2.5 m/s (D) -1.8 m/s
Q3. Two projectiles 1 and 2 are launched simultaneously from the ground with initial speeds u₁ = 20 m/s at
θ₁ = 30° and u₂ = 20 m/s at θ₂ = 60° above horizontal in the same direction. What is the path (trajectory)
of projectile 2 as seen by projectile 1 during their time in flight?
(A) Parabola (B) Straight line angled to horizontal
(C) Vertical straight line (D) Circle
Q4. Particle A moves with constant velocity vA = 10î m/s from origin (0,0). Particle B moves with constant
velocity vB = -10ĵ m/s from initial position (0, 100 m). What is the minimum distance (distance of closest
approach) between them?
(A) 50 m (B) 50√2 m
(C) 100 m (D) 25√2 m
Q5. A platform is moving horizontally with a constant velocity of 5 m/s. A projectile is launched from this
platform with a velocity of 20 m/s relative to the platform at an angle of 30° to the platform. What is the
total horizontal velocity component of the projectile relative to the ground?
9TH-CO IIT_PHYSICS 1|Pa ge
, NARAYANA CO PROGRAM 9TH CLASS PHYSICS COREQUEST
(A) 10√3 m/s (B) (10√3 + 5) m/s
(C) (10 + 5√3) m/s (D) 15 m/s
Q6. Two bodies are projected simultaneously from the same point in space with speeds u₁ = 10 m/s and u₂ =
10 m/s in directions making angles 30° and 60° with the horizontal respectively. Find the distance
between them after t = 1 s. (g = 10 m/s²)
(A) 10(√3 - 1) m (B) 10√(2 - √3) m
(C) 10 m (D) 5√2 m
Q7. A ship A is moving westwards at a speed of 10 km/h and a ship B 100 km south of A is moving
northwards at 10 km/h. How long will they take to reach the distance of closest approach?
(A) 2.5 hours (B) 5.0 hours
(C) 7.07 hours (D) 10.0 hours
Q8. For two projectiles projected from two different points in the same vertical plane to collide in mid-air,
which of the following conditions MUST be satisfied?
(A) Their horizontal components of velocity (B) Their vertical components of relative
must be equal. velocity must be zero at all times.
(C) The relative velocity vector must be initially (D) Their ranges must be equal.
irected along the line joining the two points.
Q9. A cart moves horizontally with a constant acceleration a₀ = 2 m/s². A ball is thrown vertically upward
relative to the cart with speed 10 m/s from the cart floor. What is the horizontal distance between the
ball and the launch point on the cart when the ball returns to the cart floor? (g = 10 m/s²)
(A) 2 m (B) 4 m
(C) 0 m (D) 8 m
Q10. Two particles A and B move with constant speeds v₁ and v₂ along two mutually perpendicular straight
paths intersecting at O. At t = 0, they are at distances x₁ and x₂ from O and moving towards O. The time
when they are closest to each other is:
(A) (x₁v₁ + x₂v₂) / (v₁² + v₂²) (B) (x₁v₂ + x₂v₁) / (v₁² + v₂²)
(C) (x₁v₁ - x₂v₂) / (v₁² + v₂²) (D) √(x₁² + x₂²) / √(v₁² + v₂²)
SECTION B: DIFFICULT LEVEL QUESTIONS (Q.11 to Q.20)
9TH-CO IIT_PHYSICS 2|Pa ge
