Question

A ship is travelling due west at 9kmph. What must be the velocity of second ship heading in the direction 37° west of north, if it is always due north from the first ship?

Answer 1

Use, vector concept to solve this type of question easily ,
Let first Ship A and 2nd ship B .
VA = - 9 i
Let velocity of ship B = u
VB = -usin37°i + ucos37° j
= -u × 3/5 i + u× 4/5 j
= -3u/5 i + 4u/5 j

now, velocity of A with respect to B
VBA = VA- VB
= -9i -{ -3u/5 i + 4u/5 j }
= (3u/5 - 9)i - 4u/5 j

A/C to question,
VBA is always in North direction so,
( 3u/5 - 9) = 0
3u/5 = 9
u = 15 km/h

hence, velocity of 2nd ship = -15 × 3/5 i
+ 4/5 × 15 j = -9i + 12j

Answer 2

Hi Friend,

Here is your answer,


Let Ship A and ship B .

VA => - 9 i 

We will take as velocity of ship B as = u 

VB = -usin37°i + ucos37° j 
=> -u × 3/5 i + u× 4/5 j
=> -3u/5 i + 4u/5 j 

 velocity of A and the velocity of B is,

VBA => VA- VB 

=> -9i -( -3u/5 i + 4u/5 j )

=> (3u/5 - 9)i - 4u/5 j 

SO, ACCORDING TO THE QUESTION,

VBA IS IN NORTH DIRECTION,

( 3u/5 - 9) => 0 

3u/5 => 9 

u => 15 km/h 

Therefore,the velocity of the second ship => -15 × 3/5 i + 4/5 × 15 j => -9i + 12j



Hope it helps you!

Good Luck!