SS1 Second Term Further Mathematics Lesson Note – Relative Velocity

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WEEK 6

TOPIC: RELATIVE VELOCITY

CONTENT:

1. Displacement/Relative displacement
2. Acceleration
3. Relative velocity
4. Motion of word problem

SUB – TOPIC: Relative velocity

Every object or occurrence (be it real or abstract) is relative to some other object, occurrence. If a ship has a speed of 10m/s in still water, then we are referring to its speed relative to earth.

Note the following points when solving relative velocity problems:

1. Identify the parameters in the problem i.e. relative velocity, magnitude, direction.
2. Draw the displacement diagram.
3. Write the relative velocity equation, making use of the Domino rule; e.g. _AV_B =_AV_E+_EV_Be. the velocity of A relative to B is equal to the velocity of A relative to the earth plus velocity of earth relative to B. This rule can be extended to any number of terms.

Example 1: Ship A is sailing due East at 12m/s and ship B is sailing due North at 16m/s. Find the velocity of ship B relative to ship A.

Solution:

Magnitude                       Direction

_AV_E                         12m/s                   –           East

_BV_E                                           16m/s                   –           North

Since _BV_E = _BV_A  + _AV_E    and we seek _BV_A, then _BV_A = _BV_E  – _AV_E

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