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# Two Ships moving one at 3i+4j km/hr, the other at 12i-5j km/hr - PowerPoint PPT Presentation

Two Ships moving one at 3i+4j km/hr, the other at 12i-5j km/hr. Q) When will the ships be 20 km apart?. Step 1: Draw a diagram. Ship A. 3i+4j. Ship B. 12i-5j. After 1 hour, mark their positions. Ship A. 3i+4j. Ship B. 12i-5j.

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### Two Ships moving one at 3i+4j km/hr, the other at 12i-5j km/hr

Q) When will the ships be 20 km apart?

Ship A

3i+4j

Ship B

12i-5j

Ship A

3i+4j

Ship B

12i-5j

The length of the green line is the distance between both ships!

Ship A

3i+4j

The length of the green line is

again the distance between them

Ship B

12i-5j

Watching both ships in this manner, it is difficult to determine when the green line is 20 km long.

• A better method is to find the velocity of B relative to A, and to look at A on this diagram.

• VA = 3i+4j

• VB = 12i-5j

• VBA = VB – VA = (12i-5j)-(3i+4j) = 9i-9j

• This was the green line on the previous diagram

If the origin is at A, and moving with A, then the length of the green line is easy to find.

Ship A

3i+4j

VBA = 9i-9j from Ship A

It is easier to draw a separate diagram to show the velocity of B relative to A, i.e., the green line above.

Ship B

12i-5j

Relative Diagram the green line is easy to find.

In this Diagram, Ship A is stationary and Ship B is moving at 9i-9j.

(In actual fact, the origin of this diagram is moving with Ship A, and the green line denotes the distance B is from A)

The speed of B relative to A is 12.7 km/hr.

So they will be 20 km apart after 20÷12.7 = 1.57 hrs = 1hr 34 mins.

VBA = 9i-9j

If you want to know how far A and B have moved from their starting points at this time, take this time back to the original diagram.

Ship A the green line is easy to find.

3i+4j

The speed of ship A is 5 km/hr . After 1.57 hrs, Ship A has moved a distance of 5×1.57 = 7.85 km

The speed of Ship B is 13 km/hr . After 1.57 hrs, Ship B has moved a distance of 13×1.57 = 20.41 km

You should now use the Cosine rule

To confirm that the distance between

them is indeed 20 km.

Ship B

12i-5j