Hello, carlasader!

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 .

Then: .

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.

If

Square both sides: .

Factor: .

Therefore, they are 300 m apart (again) when seconds.