1. ## a question about differentiation

P is a point 22m due east of a fixed point O and Q is a point 14m due south of O. A particle A starts at P and moves towards O at a speed of 4m/s while a particle B starts at Q at the same time as A and moves towards O at a speed of 3m/s. Find an expression for the distance between A and B t seconds after the start. Hence, find the value of t when the distance between A and B is a minimum and find this minimum distance.

i can't figure out how to relate them and make an expression.
i think i can do the latter part once the expression is found.

2. Hi

First define a referential : for instance O as origin, x axis = (OP) with P abscissa = 22, y axis = (OQ) with Q ordinate = -14, and time=0 when the particles start. Then P(22,0) and Q(0,-14).

The first particle speed is $\overrightarrow{v_1} = -4\overrightarrow{i}$
Integrating gives $\overrightarrow{OM_1}= (-4t+22)\overrightarrow{i}$

Same method for the second particle.

Then $\overrightarrow{M_1M_2} = -\overrightarrow{OM_1} + \overrightarrow{OM_2}$

Then the distance $M_1M_2$