Kinematics part-3 Relative motion questions with solutions

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• MCQmediumKinematics part-3 Relative motionRelative motion in one dimension

  A swimmer and a freely floating raft are together at an instant in a river. The swimmer immediately swims upstream with speed u relative to water for time T, then turns instantly and swims downstream with the same relative speed. After turning, the time required to meet the raft again is:

  Options

  • Option A

    T

  • Option B

    2T

  • Option C

    [(u + v)/(u - v)]T

  • Option D

    [(u - v)/(u + v)]T

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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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• A/ReasyKinematics part-3 Relative motionRelative motion in one dimension

  Evaluate the following statements.

  Assertion

  Assertion (A): Two freely moving particles near Earth's surface can have zero relative acceleration even though each has non-zero acceleration.

  Reason

  Reason (R): If both particles experience the same gravitational acceleration g⃗, then a⃗_AB=a⃗_A-a⃗_B=0.

  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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• Multi-correctmediumKinematics part-3 Relative motionRelative motion in one dimension

  Two particles A and B are simultaneously projected vertically upward from the same point with speeds u and 2u. Neglect air resistance and consider the interval while both remain in free flight. Which statements are correct?

  Select all that apply

  • Option A

    Their relative acceleration is zero

  • Option B

    Their relative velocity is constant

  • Option C

    Their separation increases linearly with time

  • Option D

    They meet again in air before A returns to the launch point

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• MCQeasyKinematics part-3 Relative motionRain problem and relative approach problem

  Rain falls vertically downward with speed 20 m/s. A man runs horizontally at 15 m/s. The speed of rain relative to the man is:

  Options

  • Option A

    5 m/s

  • Option B

    20 m/s

  • Option C

    25 m/s

  • Option D

    35 m/s

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• MCQmediumKinematics part-3 Relative motionRain problem and relative approach problem

  A fixed inclined plane makes 30° with the horizontal. A man starts from rest and accelerates down the plane with constant acceleration 4 m/s². Rain falls vertically downward at 20 m/s. At what time will the velocity of rain relative to the man be perpendicular to the inclined plane?

  Options

  • Option A

    2.0 s

  • Option B

    2.5 s

  • Option C

    5/√3 s

  • Option D

    5.0 s

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• MCQdifficultKinematics part-3 Relative motionRain problem and relative approach problem

  Rain falls vertically downward with speed v. An inclined plane making angle α above the horizontal moves horizontally with speed u. The magnitude of the component of rain velocity relative to the plane normal to its surface is:

  Options

  • Option A

    |v cosα - u sinα|

  • Option B

    |v sinα - u cosα|

  • Option C

    v cosα + u cosα

  • Option D

    √(u² + v²)

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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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• MCQdifficultKinematics part-3 Relative motionRain problem and relative approach problem

  Rain falls vertically downward with speed u. A man starts from rest and moves horizontally with constant acceleration a. If θ is the apparent angle of rain measured from the vertical at time t, then:

  Options

  • Option A

    tanθ = u/(at)

  • Option B

    tanθ = at/u

  • Option C

    tanθ = a/(ut)

  • Option D

    tanθ = ut/a

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

  Point B is 120 m perpendicular from a straight road and its foot P is 500 m along the road from A. Speed on road is 10 m/s and through field is 6 m/s. For minimum time, if CP=N m, find N.

  Your answer

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