Relative Motion

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Rain falls vertically at 6 m/s. Person runs east at 8 m/s. Relative velocity components of rain w.r.t runner are:

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6 m/s vertical, 8 m/s horizontal

8 m/s vertical, 6 m/s horizontal

10 m/s vertical, 6 m/s horizontal

6 m/s vertical only

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Subject: physics
Chapter: kinematics
Topic: relative motion
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

6 m/s vertical, 8 m/s horizontal

Let the vertical (down) direction be $- \hat{j}$ and east be $+ \hat{i}$ .

Velocity of rain $v_{r} = - 6 \hat{j} m/s$
Velocity of person $v_{p} = 8 \hat{i} m/s$ Relative velocity of rain with respect to person is: $v_{r p} = v_{r} - v_{p} = - 6 \hat{j} - 8 \hat{i} m/s$ . The components are:
Vertical component: $6 m/s$
Horizontal component: $8 m/s$ (Magnitude would be $6^{2} + 8^{2} = 10 m/s$ at an angle).

This medium difficulty physics question is from the chapter kinematics, covering the topic of relative motion. It appeared in the 2025 exam.

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Relative Motion

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