Here's #7 . . .
7. Two cars A and B are moving on straight horizontal roads with constant velocities.
The velocity of A is 20 m/sec due east, the velocity of B is m/sec,
where and are unit vectors directed due east and due north, respectively.
Initially A is at the origin O, and the position vector of B is .
At time seconds, the position vectors of A and B are and , resp.
a) Find expressions for and in terms of .
We have: .b) Hence write an expression for in terms is .
Since B is always on a bearing of 45°, this occurs when:c) Find the time when the bearing of B from A is .
. . Then: . seconds.
The distance is: .d) Find the time when the cars are again 300 m apart.
Square both sides: .
Therefore, they are 300 m apart (again) when seconds.