Relative motion in 2-D and shortest distance problem questions with solutions

Showing 1–10 of 73 questions

• Multi-correctmediumKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A and B move with constant velocities in a plane. In the inertial frame moving with A, which statements are correct?

  Select all that apply

  • Option A

    A is at rest

  • Option B

    B moves with velocity v⃗_B-v⃗_A

  • Option C

    Minimum separation is the perpendicular distance from A to B's relative trajectory if the perpendicular foot lies at future time

  • Option D

    Changing to A's inertial frame changes the physical minimum separation

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• Multi-correctdifficultKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  An object has velocity magnitude v₁ with respect to ground. An observer moving with constant velocity magnitude v₀ with respect to ground measures the object's velocity magnitude as v₂. Which relation must be true?

  Select all that apply

  • Option A

    v₀ ≥ v₁+v₂

  • Option B

    v₁ ≤ v₂+v₀

  • Option C

    v₁ ≥ v₂+v₀

  • Option D

    All of the above

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• MCQmediumKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A particle is projected from point A at 60° with speed 10√3 m s⁻¹. At the same time the wedge shown moves right at 10√3 m s⁻¹. Find the time after which the particle strikes the wedge.

  

  Options

  • Option A

    2 s

  • Option B

    2√3 s

  • Option C

    4/√3 s

  • Option D

    None of these

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• A/ReasyKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  Evaluate the following statements.

  Assertion

  Assertion (A): At closest approach, the relative velocity of two particles need not be zero.

  Reason

  Reason (R): At closest approach only the component of relative velocity along the instantaneous line joining the particles must vanish.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• NumericmediumKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A is projected from origin with velocity (10î+20ĵ) m/s. Simultaneously B is projected from (30,40) m with velocity (4î+12ĵ) m/s. Both experience the same gravity. If their relative trajectories predict collision after N seconds, find N.

  Your answer

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• Multi-correctmediumKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  Two particles move with constant velocities in a plane. Initially B relative to A has position $\vec{r}$₀ and velocity $\overrightarrow{V}_{r}$ Which statements are correct?

  Select all that apply

  • Option A

    For an exact future collision r⃗₀×v⃗_r=0 is necessary

  • Option B

    For a future collision r⃗₀·v⃗_r<0 is required

  • Option C

    If r⃗₀·v⃗_r=0, they are at a stationary separation at that instant

  • Option D

    If r⃗₀×v⃗_r≠0, exact collision is impossible but a finite closest approach may occur

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• Multi-correctmediumKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  Two particles move with constant velocities in a plane. From A, B is continuously observed along the same bearing while AB is decreasing. Which statements are correct?

  Select all that apply

  • Option A

    They are on a collision course

  • Option B

    Relative velocity is parallel to the separation vector

  • Option C

    r⃗_BA×v⃗_BA=0

  • Option D

    Minimum separation must be non-zero

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• Multi-correctdifficultKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A man on a cart moving along a straight line throws a ball vertically upward with respect to himself. Which statements are correct?

  Select all that apply

  • Option A

    The ball will always return to him.

  • Option B

    The ball will never return to him.

  • Option C

    The ball will return to him if the cart moves with constant velocity.

  • Option D

    The ball will fall behind him if the cart has positive acceleration.

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• ParagraphdifficultKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A car is moving south at 20 m s⁻¹. A motorcyclist is moving east at 15 m s⁻¹. At a certain instant, the motorcyclist is due south of the car and is 50 m away from it.

  Sub-question 1

  The shortest distance between the motorcyclist and the car is:

  Options

  • Option A

    20 m

  • Option B

    10 m

  • Option C

    40 m

  • Option D

    30 m

  Sub-question 2

  The time after which they are closest to each other is:

  Options

  • Option A

    13 s

  • Option B

    8/3 s

  • Option C

    1/5 s

  • Option D

    8/5 s

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• MCQeasyKinematics part-3 Relative motionRelative motion in 2-D and shortest distance problem

  A mouse moves indefinitely along a straight line with speed u. A cat starts off the mouse's line and always runs directly towards it with constant speed v. Which condition guarantees eventual capture?

  Options

  • Option A

    v>u

  • Option B

    v=u

  • Option C

    v<u

  • Option D

    Any v>0

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