Qualification > Math

Add math doubt...astar plz help

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Theguitarist:
Ok, I will answer this question.

(i) If u look closely it says that the ship sails 'north east'. hence its unit vector north east will be (i+j)/ square root of 2. And since velocity has both speed and direction, its velocity = 15* square root of 2 * the unit vector which = 15i + 15j

(ii) Since we have established that the velocity in the stated direction is 15i + 15j, the distance it has traveled at 10:30 can be found by multiplying 1.5 into the velocity. which = 22.5i + 22.5j. But since they have asked for the position vector, it will be equal to 22.5i + 22.5j + 2i + 3j = 24.5i + 25.5j

(iii) Similarly for part three; the distance travelled t hours after leaving = (15t)i + (15t)j. Hence in terms of 't' the position will be = (15t + 2)i + (15t + 3)j

(iv) In this subquestion they have simply asked for the velocity of the ship relative to the submarine (Vssu) = Velocity of ship - Velocity of submarine = 
        (15i + 15j) - (25j). NOTE: 25j is because it is only travelling north. = 15i -10j

Answer to final part in the next post

Theguitarist:
Assuming t = the time when the two bodies meet.

After 't' hours the position vector of the ship = (2 + 15t)i + (3+ 15t)j

After 't' hours the position vector of the submarine = 47i + (-27+ 25t)j.

At their point of collision, the position vectors should be the same. Hence to find 't' we equate: 47 = 2 + 15t. Therefore, t = 3 hours

Hence final position vector can be found by substituting t in any one of the position vectors which should be 47i + 48j.

Hope that helped!

astarmathsandphysics:
I will try it tomorrow. I cant download it to my phone and open it.

astarmathsandphysics:
Thamks guitarman

Ghost Of Highbury:
why will it be i+j/root 2
didnt get the first part itself?

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