Answer:

time t=0,the first particle is 300cm from O and moving toward O at a velocity of 20cm/s.

The distance of this particle to O as a function of time is:

A=300−20t

At the time t=0, the second particle is 400CM from O and moving toward O at a velocity of 20m/s.

The distance of this particle to O as a function of time is:

B=400−20t

The distance between the 2 particles can be found using the cosine rule

C

2

=A

2

+B

2

−2ABcos60

0

C

2

=(300−20t)

2

+(400−20t)

2

−2(300−20t)(400−20t)cos60

0

C

2

=(400t

2

−12000t+90000)+(400t

2

−16000t+160000)−(400t

2

−14000t+120000)

C

2

=400t

2

−14000t+130000

C=

(400t

2

−14000t+130000)

Now one needs to find t such that C will be minimized.

If C is minimized at a certain t, then also C

2

will be minimized at that t.

So INSTEAD of finding the first derivative of C (which is a square root,

so a lot of work), one can simply find the first derivative of C

2

(a

quadratic expression, which is a lot LESS work)

C

2

=400t

2

−14000t+130000

dt

2

dC

2

=800t−14000

800t−14000=0

t=17.5s

At time t=17.5s the distance between the 2 particles is minimized.

The distance at that time will be:

C=

(400×17.5

2

−14000×17.5+130000)

C=

7500

⇒C=50

3