[In this question, the unit vectors i and j are due east and due north respectively:] A particle P is moving with constant velocity (–5i + 8j) m s–1 - Edexcel - A-Level Maths Mechanics - Question 6 - 2008 - Paper 1

The direction of the velocity vector can be found by determining the angle using the inverse tangent function:

heta = an^{-1} rac{8}{-5}

Since the vector is in the second quadrant (because the x-component is negative and the y-component is positive), we need to adjust the angle to find the bearing:

heta = 180° + an^{-1} rac{8}{5} \\ = 180° - heta = 360° - ext{atan}(8/5) \\ ext{Bearing} = 328°

At time t = 3 s, we need to find the position vector of P:

$$ext{p.v. of P} = (7i - 10j) + 3(-5i + 8j) = 7i - 10j - 15i + 24j = -8i + 14j$$

At t = 3 s, the velocity for P is (u + vi) m/s:

Since it also passes through O (origin) after 4 seconds, we find that:

$$$$

To find the total time taken, we compute the time taken to reach due south of A. The only southward movement is in the y-direction and P travels from (7, -10) to (7, y):

The displacement can be calculated as:

$$$$

Therefore, total time taken = 3 (initial) + 4 (in the new velocity) + 3 (for southward) = 10.5 s.