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Vector Addition and Relative Velocity

conceptmedium~45 min study9 MCQ

Vectors add by the triangle or parallelogram rule; the velocity of A relative to B is vAB = vA - vB.

Practice 9 questionsBack to syllabus~14 min

What is Vector Addition and Relative Velocity?

Vectors add by the triangle or parallelogram rule; the velocity of A relative to B is vAB = vA - vB.

Key formula / rule: Resultant of P and Q: R = √(P2 + Q2 + 2PQ cos t).

Key points

  • Compute the resultant of two vectors analytically.
  • Model a river-boat or rain-man situation using relative velocity.

Common exam trap

Adding vector magnitudes arithmetically instead of vectorially.

Definitions

Term

Vector Addition and Relative Velocity

Meaning

Vectors add by the triangle or parallelogram rule; the velocity of A relative to B is vAB = vA - vB.

Term

Vector Addition and Relative Velocity — explanation

Meaning

Two-dimensional motion becomes tractable once velocities are treated as vectors. Relative velocity converts river-boat, rain-man and overtaking problems into a single subtraction performed component-wise.

Learning objectives

  • Compute the resultant of two vectors analytically.

  • Model a river-boat or rain-man situation using relative velocity.

Formulae

Key point

Resultant of P and Q: R = √(P2 + Q2 + 2PQ cos t).

Key point

vAB = vA - vB, and vBA = -vAB.

Key point

Component-wise subtraction is safer than drawing for exam speed.

Prerequisites

  • PHY-U1-KIN-T1-S1-C2

Common mistakes

  • Adding vector magnitudes arithmetically instead of vectorially.

  • Reversing the order of subtraction in relative velocity.

Keywords

  • Vector

  • Addition

  • Relative

  • Velocity

Practice preview

  • If v_A is the velocity of object A and v_B is the velocity of object B, what is the velocity of A relative to B?…

    easy

  • A man is walking due East with a velocity of 3 km/h. Rain appears to be falling vertically downwards with a velocity of 4 km/h to him. What is the actual velocity of the rain?…

    medium

  • A boatman wants to cross a river of width 500 m. The river flows at 5 m/s. The boat can travel at 10 m/s in still water. If the boatman wants to cross the river in the shortest possible time, what is the time taken and h…

    hard

Practice 9 questions