How to find the distance？Vector

In this question the origin is taken to be at a harbour and the unit vectors i and j to have lengths of 1km in the directions E and N.

A cargo vessel leaves the harbour and its position vector t hours later is given by - r1 = 12ti + 16tj

A fishing boat is trawling nearby and its position at a time t is given by - r2 = (10 - 3t)i + (8+4t)j

Questions: 1) How far apart are the two boats when the cargo vessel leaves harbour?

2) How fast is each boat traveling?

Answers: 1) 12.8km

2) 20 km per hour a 5 km per hour

Can you guys explain to me how they got these answers? Your help is much appreciated (Evilgrin)

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Re: How to find the distance？Vector

Hey Jin... from the beutiful city of Shah Alam ( Malesia)......

the problem you posted is very easy ...it seems to me that you have no idea what is all about....

Anyway put t =0 in the first equation and you will get the vector r1=0 this means that at t=0 it leaves the harbor....

at the same time the vector of the boat is r2=10i+8j get the magnitude of this vector and you will get |r2| =sqr(10^2+ 8^2)=10.8 Km ....as simple as such...

for the second question : the vector can be written r1=t(12i+16j) or r1=tv where v=12i+16j and this is the vector of the speed for the cargo vessel....now grt the magnitude of this vector |v|=sqr(12^2+16^2)=20 km/h

do the same for the Boat to find 5km per hour.

Please study this chapter more

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Re: How to find the distance？Vector

For (1) it's important to recognize that the cargo vessel leaves the harbor at t=0. Do you see why this is true? So you can plug in t=0 and get the location of the fishing vessel (in terms of i and j). From there, you do as MINOANMAN said.

For (2), MINOANMAN has given you the answer. You just take the derivative of the position vector for the boat and the cargo vessel.

Hope this helps,

Hollywood

- Hollywood