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

Showing 1–10 of 73 questions

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

  A bird flies south at 40 km h⁻¹ and a train moves east at 40 km h⁻¹. The velocity of the bird relative to an observer in the train is:

  Options

  • Option A

    40√2 km h⁻¹, north-east

  • Option B

    40√2 km h⁻¹, south-east

  • Option C

    40√2 km h⁻¹, south-west

  • Option D

    40√2 km h⁻¹, north-west

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

  A boat has speed u relative to water in a river of speed v, with u > v. First it is aimed perpendicular to the bank; its crossing time is t₁. Next it is aimed upstream so that it reaches the point directly opposite; its crossing time is t₂. Then t₂/t₁ equals:

  Options

  • Option A

    √(1 - v²/u²)

  • Option B

    1/√(1 - v²/u²)

  • Option C

    1 - v/u

  • Option D

    1 + v/u

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

  A is projected from ground with velocity (20î+30ĵ) m/s. Simultaneously B is projected from a point 40 m vertically above A with velocity (30î+20ĵ) m/s. While both are in free flight, which statements are correct?

  Select all that apply

  • Option A

    Relative acceleration is zero

  • Option B

    v⃗_BA=10î-10ĵ is constant

  • Option C

    Relative trajectory is a straight line

  • Option D

    Their individual parabolic trajectories must be parallel

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

  A straight road passes through A. Point B is perpendicular distance d from the road, and its foot P is distance L along the road from A. A person moves on road at speed v and through field at speed v/n (n>1). He leaves road at C before P; let CP=x. The minimum-time condition is:

  Options

  • Option A

    x/√(x²+d²)=1/n

  • Option B

    x/√(x²+d²)=1/n²

  • Option C

    x/d=n

  • Option D

    d/√(x²+d²)=1/n

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

  Two particles A and B move with constant velocities $\overrightarrow{v}_1$and $\overrightarrow{v}_2$. At the initial moment their position vectors are $\overrightarrow{r_1}$ and $\overrightarrow{r}_2$ respectively. The condition for particles A and B to collide is:

  Options

  • Option A

    ($\vec{r}_1-\vec{r}_2$)/|$\vec{r}_1-\vec{r}_2$| = ($\vec{v}_2-\vec{v}_1$)/|$\vec{v}_2-\vec{v}_1$|

  • Option B

    $\vec{r}_1.\vec{v}_1$= $\vec{r}_2.\vec{v}_2$

  • Option C

    $\vec{r}_1$×$\vec{v}_1$=$\vec{r}_2$×$\vec{v}_2$

  • Option D

    $\vec{r}_1-\vec{v}_1$= $\vec{r}_2-\vec{v}_2$

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

  An aeroplane is observed by two persons travelling at 60 km h⁻¹ in opposite directions along a straight road. To one observer the plane appears to cross the road at right angles; to the other it appears at 45°. At what angle θ does the plane actually cross the road?

  

  Options

  • Option A

    45°

  • Option B

    tan⁻¹2

  • Option C

    tan⁻¹4

  • Option D

    tan⁻¹8

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

  Two particles are thrown simultaneously from points A and B with constant velocities u₁=2 m s⁻¹ and u₂=14 m s⁻¹ respectively, as shown in the figure.

  

  Sub-question 1

  The relative velocity of B as seen from A is:

  Options

  • Option A

    -8√2î+6√2ĵ m s⁻¹

  • Option B

    4√2î+3√3ĵ m s⁻¹

  • Option C

    3√5î+2√3ĵ m s⁻¹

  • Option D

    3√2î+4√3ĵ m s⁻¹

  Sub-question 2

  The acute angle with the horizontal at which B appears to move as seen from A is:

  Options

  • Option A

    37°

  • Option B

    53°

  • Option C

    15°

  • Option D

    90°

  Sub-question 3

  The minimum separation between A and B is:

  Options

  • Option A

    3 m

  • Option B

    6 m

  • Option C

    12 m

  • Option D

    9 m

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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

  Ship A moves due east at 5 km h⁻¹. Ship B heads 30° east of north. What should be B's speed so that B remains always due north of A?

  Options

  • Option A

    10 km h⁻¹

  • Option B

    9 km h⁻¹

  • Option C

    8 km h⁻¹

  • Option D

    7 km h⁻¹

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