Mechanics Assignment, please someone help me with this question?

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Princess Kasumi

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1. A destroyer sights a ship travelling with constant velocity 5j, whose position vector at the time of sighting is (6000i + 2000j) relative to the destroyer. The destroyer immediately begins to move with velocity
k(4i + 3j), where k is a constant, in order to intercept the ship.

(a) Find k and T, the time to interception.

The ship's radar located the destroyer at time 1/2 T and it immediately changes its course so that it is moving with velocity (i + 5j). The destroyer continues with its original velocity.

(b) Find the distance between the ship and the destroyer at time T.
 
a)
6000i+(2000+5T)j=Tk(4i+3j)

4Tk=6000
3Tk=2000+5T

Tk=1500 ...substitute..
4500=2000+5T-->T=500
4*500*k=6000-->k=3

b)
1/2 T=250
ship position-->
6000i+(2000+5*250)j=
6000i+3250j
destroyer position-->
Tk(4i + 3j)=750(4i+3j)=
3000i+2250j

final ship position-->
6000i+3250j+250(i+5j)=
6250i+4500j
final destroyer position-->
1500(4i+3j)=
6000i+4500j
distance between
the ship and the dstroyer-->250
 
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