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**Projectory: Super Hard Apparently From The Military!!!!!!! Gah Hard**

hey all i got a very difficult question, apparantly some guy from the military working with projectory wrote this and below is the questions and i could not do sections 7 & 8 at all below i have posted my answers not sure if theya re right please check them for me THANKS!!!!!!!!

In a war games scenario a ship, the “Dominant”, protects a region by describing a course such that its position at any time relative to a fixed point O is given by

r(D) = (10 + 10cos(nt))i + 10sin(nt)j

where n is a positive constant and 1 unit represents a distance of 10km and it is measured in hours after noon on Friday 2nd Sep local time

1. Find the Cartesian equation of the path of the Dominant and sketch it neatly on a graph of appropriate size. Indicate the direction of the ship on the graph.

**** my ANS: Circular motion **********

2. Find the speed of the dominant at any time in terms of n.

**** MY ANS: 10n Units/hour **********

At t = 0 a radar contact is picked up by the dominant. The contact is determined to be a ship, the “enemy” and its course is estimated to be such that is position at any time t is given by

r(E) = ti – 2tj

3. Find the Cartesian equation of the path of the Enemy and sketch its graph on the same axes drawn previously.

**** MY ANS: Y = -2x ***************

4. What is the speed of the enemy?

**** MY ANS: √5 units/hour *************

5. Find the point(s) where the paths of the Dominant and Enemy cross.

**** MY ANS: (0,0) and (4,8) *********

6. Find the first two values of n, correct to 4 decimal places, for which D and E will collide and what would be the distances covered by each ship from noon until they collide.

**** MY ANS: N = 1.0172 and 2.5880 ***************

7. Using the lowest value of n for collision and if the Dominant fires a missile at t = half the collision time, calculate the path of the missile if it is to destroy the enemy, given that the missile flies at a horizontal speed of 1 km/s.

(I think they are asking for position vector but I am not 100% sure)

CANT DO!!!!!!!!!!

8. The enemy engages its radar systems and makes a move. At t = a third of the collision time, the enemy moves 150º true bearing and travels 50% faster than its original speed in an attempt to escape. Given that the Dominant still fires a missile at t = half the collision time, find the path of the missile if it is to hit the destroyer. Missile still flies at a horizontal speed of 1 km/s.

CANT DO!!!!!!!!!!