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Please help with As level mechanics question?

Please explain part b, I understand part A but part B is confusing me too much. I've spent too long on it. Thank you.

A boat is travelling in water that is moving north-east at a speed of 2 m s1 . The velocity of the boat relative to the water is 5 m s1 due west.

(a) Show that the magnitude of the resultant velocity of the boat is 3.85 m s1 , correct to three significant figures. (4 marks)
(b) Find the bearing on which the boat is travelling, giving your answer to the nearest degree. (4 marks)

Reply 1

Zacken

Original post by Jas1947

Please explain part b, I understand part A but part B is confusing me too much. I've spent too long on it. Thank you.

Have you? Post your workings then.

Reply 2

Minnie16

Attachment not found

Original post by Zacken

Have you? Post your workings then.

Im sorry theyre sideways, i boxed the markscheme answer in pink

(edited 7 years ago)

1466422209528-114116516.jpg317.5KB

1466422261591-869774595.jpg285.2KB

Reply 3

ghostwalker

Original post by Jas1947

Im sorry theyre sideways, i boxed the markscheme answer in pink

Your problem stems from an incorrect diagram.

Here's the basics - resultant in green:

(edited 7 years ago)

Reply 4

Minnie16

Original post by ghostwalker

Your problem stems from an incorrect diagram.

Here's the basics - resultant in green:

But im still struggli

ng to get the correct answer, could some one please post their own working ?

Reply 5

ghostwalker

Original post by Jas1947

But im still struggli

ng to get the correct answer, could some one please post their own working ?

Your virtually there.

Your new problem is the sine rule. It does not distinguish between the angle x and the angle 180-x - they both have the same sin. This is something to be aware of if you use the sine rule.

In this case the angle is obtuse and you want 180 - 66.68.

Use of cosine rule would have avoided the ambiguity. Sine rule would be fine if you recognized it was an obtuse angle and acted accordingly.

Reply 6

Minnie16

Original post by ghostwalker

Im sorry i dont understand

Reply 7

ghostwalker

Original post by Jas1947

Im sorry i dont understand

Consider the shape of the sine curve. It increases from 0 to 90 and then decreases from 90 to 180,

If x is an angle between o and 90, then there is a corresponding angle 180-x, and they both have the same sine, sin(x) = sin(180-x). e.g. sin(30) = sin(150).

So, when you use the sine rule, and get sin(x) = 0.5 say, then x = 30 OR possibly x = 150 (that is 180-30). You don't know. You have to rely on the geometry of the situation to distinguish between the two values.

In this case the angle at A is actually obtuse, i.e greater than 90, so your angle is 180- "the angle you worked out".