help?

ted9308

Q In a desert a tank travels x km on a bearing of 50 degrees from a base o then ykm on a bearing of 140 degrees to a bunker b..calculate the magnitude and direction of the displacement vector OB when x = 7 and y = 6?

My attempt so far has included drawing a diagram which i turned into a triangle which can't possibly be right as the sum of angles in a triangle add up to 180?..Can i transform this into another shape or is it simply that it is multiple shapes as it does not state the direction?

bnt

Well, each "leg" is a vector, and if you draw the vectors end-to-end, you have two sides of a triangle. Remember that the given angles are bearings i.e. anti-clockwise from North=0°. Say you draw (to scale):
O-A = 7km @ 50° relative to North
then
A-B = 6km @ 140° relative to North
you can then draw O-B and complete the triangle. The 180° thing applies to the internal angles in the triangle, but that's not what's being asked here - don't worry about it. The answer is the length of O-B, and its bearing relative to North.

There is a mathematical way of doing it too, but I don't know whether you've covered the maths yet. Do you know about Rectangular vs Polar notation? If I do this kind of question. I convert the given Polar vectors to Rectangular form, add them, and convert the result back to Polar. I get

9.22km @ 90.6°