Speed Reading Course

what do apparent path and interception mean in relative velocity?

i am really lost on relative velocity. i don’t even know how to draw the vector diagrams correctly, i feel so stupid. i don’t seem to get the bearing correct, the angles and almoost everything that needs to be know for relative velocity. maybe i shall quote a simple qns so we can start on it step-by-step, so that i can understand it?

(a) Speed and direction of Q relative to P

This question is asking about the speed and direction of Q’s motion assuming that P is ‘stationary’ (in the relative sense).

You need to draw a vector diagram and deduce the resultant vector, which is vq – vp.

The step-by-step procedure to draw the vector diagram is:
(1) Draw the vector depicting Q’s motion i.e. 4m/s at 60° to the vertical, pointing approximately NW.
(2) Continue from the tip of the vector of Q, draw the vector depicting P’s motion in the Opposite sense i.e. 3m/s towards East.
(3) Draw the resultant vector connecting the start point of Q to the end point of P.

If you draw the vector diagram to scale, you can measure the length of the resultant vector and its direction. Alternatively, you can also apply trigonometry to deduce the answers.

(b) Distance between P and Q when Q is due East of P.

(1) Calculate the time taken for Q to move 2km towards North.

We are given that Q is moving at 4m/s at 60° West of North. Therefore, Q is moving at 2m/s northwards (i.e. 4m/s x cos60°).
The time taken for Q to move 2km northwards is 1000s (i.e. 2000m / 2m).

(2) Calculate the distance Q travelled westwards after 1000s.

Distance travelled is 3464m (i.e. 4m/s x sin60° x 1000s).

(3) Calculate the distance P travelled westwards after 1000s.

Distance travelled is 3000m (i.e. 3m/s x 1000s).

(4) Calculate the distance between P and Q.

Distance apart = 3464 – 3000 = 464m

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