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

Showing 1–10 of 32 questions

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

  For two particles with constant but different accelerations, which statements are correct?

  Select all that apply

  • Option A

    r⃗_BA=r⃗₀+v⃗_r0t+(1/2)a⃗_rt²

  • Option B

    At a stationary separation r⃗_BA·v⃗_BA=0

  • Option C

    Relative velocity is necessarily constant

  • Option D

    There may be more than one stationary value of separation

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

  For two particles moving with constant velocities, let r⃗(t)=r⃗₀+v⃗_rt. Which statements are correct?

  Select all that apply

  • Option A

    At closest approach r⃗·v⃗_r=0

  • Option B

    If r⃗₀·v⃗_r>0, they are initially moving apart

  • Option C

    $t_min=-(r⃗₀·v⃗_r)/v_r²$ for unrestricted time

  • Option D

    The perpendicular distance from origin to the relative-motion line equals |r⃗₀×v⃗_r|/|v⃗_r|

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

  A target starts at (60,80) m and moves at 6î m/s. An interceptor starts from origin and must meet it exactly after 10 s while moving with constant velocity. If required speed is 4√N m/s, find N.

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

  Two roads intersect at 60°. Car A is 80 m from O and approaches at 10 m/s. Car B is 60 m from O and approaches at 10 m/s. If unrestricted closest approach occurs after N seconds, find N.

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

  Car A is 200 m west of an intersection and moves east at 20 m/s. Car B is 400 m north and moves south at 20 m/s. If their minimum separation is 20√N m, find N.

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

  A prey moves with constant velocity along a straight line. A predator moves with constant speed and its velocity always points toward the prey's instantaneous position. Which statements are correct?

  Select all that apply

  • Option A

    Predator trajectory is generally curved

  • Option B

    Predator may have non-zero acceleration despite constant speed

  • Option C

    Predator acceleration is perpendicular to its instantaneous velocity

  • Option D

    Relative velocity must always point along the line joining predator and prey

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

  Particle A moves as r⃗_A=3tî+4tĵ and particle B moves as r⃗_B=(6+0t)î+(8+0t)ĵ. If their separation is stationary for the first positive time at t=N seconds, find N.

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

  The initial separation of two particles is d. Their constant relative velocity makes an acute angle θ with the direction opposite to the initial relative-position vector. The minimum separation is:

  Options

  • Option A

    d cosθ

  • Option B

    d sinθ

  • Option C

    d tanθ

  • Option D

    d/sinθ

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