Help on question...

A boat has a speed of 4km/h in still water and sets its course north-east in an easterly current of 3km/h. Write each velocity in component form using unit vectors i and j in directions east and north and hence find the magnitude and direction of the resultant velocity.

Plz i need help in it. cud u draw a diagram also wen answerin it coz it will help me visualise...

Thanks

Reply 1

Christophicus

18

ArsenalTFX

A boat has a speed of 4km/h in still water and sets its course north-east in an easterly current of 3km/h. Write each velocity in component form using unit vectors i and j in directions east and north and hence find the magnitude and direction of the resultant velocity.

Plz i need help in it. cud u draw a diagram also wen answerin it coz it will help me visualise...

Thanks

Boat speed = 4km/h
Boat velocity = k(i+j) km/h = (ki + kj) km/h

=> |speed|² = k² + k²
=> 4² = 2k²
=> 8 = k²
=> k = √8 = 2√2

Boat velocity = 2√2(i+j) km/h

Current speed = 3km/h
Current velocity = 3i km/h

bVc = Vb - Vc
bVc = (2√2-3)i + (-2√2)j
|bVc| = √[(2√2-3)²+(-2√2)²]
|bVc| = 2.83 km/h

Direction of bVc
tanθ = -2√2/(2√2-3)
θ = 087°

Reply 2

Cexy

The velocity of the boat is

2√2 i + 2√2 j because it needs to have the same north and east components, and this gives it a total speed of 4, as the question says.

The velocity of the water is

3 i

You need to add these together to give the final speed of the boat, which is

(3 + 2√2) i + 2√2 j

To find the resultant velocity, you square both of the components, add them together and take the square root:

V = [(3 + 2√2)² + (2√2)²]^½

V = (25 + 12√2)^½

And the direction of travel is found by using tanθ = opposite/adjacent

tanθ = 2√2 / (3 + 2√2)

So θ = tan^-1[2√2 / (3 + 2√2)]
--------------
^ You seem to have spontaneously reversed the direction of the current there. I think you need to be adding the current velocity to the boat's velocity to find the final velocity. Although you've now got me doubting myself.

Edit: And now you've deleted your post, making me look silly! :wink:

boat.jpg39.7KB

Reply 3

carol05

ArsenalTFX

Plz i need help in it. cud u draw a diagram also wen answerin it coz it will help me visualise...

Thanks

I quote the Rules.
No txt spk
Do not use text speak or CAPITALS.

I find it depressing that students can't use the proper spelling of simple words. The Rules clearly state No txt spk

Reply 4

SunGod87

7

There needs to be a rule on member moderation.

Reply 5

ArsenalTFX

OP

thanks for the answer...

and sorry, i didnt no we cant use txt speech, but you should really take a chill pill...
Getting uptight because im not speaking properly on a forum which is designed for teenage use is pretty weird :s-smilie:

(dont take offence. but i just find the rules crazy)

Help on question...

Related discussions

Articles for you