related rates?

[KataKoniK]

Hi,

Is this a question on related rates? If so, can anyone help me do this question? I have no clue on even how to start it out.


A clock has an hour hand 4cm long and a minute hand 8cm long. How fast is the distance between the tips of the hands changing at 2:00?

[arildno]

1. Describe the position vectors of the tips as follows:
\vec{r}_{hour}(t)=4(\cos(\omega_{h}t+\theta_{h,2}) \vec{i}+\sin(\omega_{h}t+\theta_{h,2})\vec{j})
\vec{r}_{min}(t)=8(\cos(\omega_{m}t+\theta_{m,2})\ vec{i}+\sin(\omega_{m}t+\theta_{m,2})\vec{j})
Here:
\omega_{h},\omega_{m} are the respective angular velocities (you should be able to figure them out by yourself).
\theta_{h,2},\theta_{m,2} are the respective angles made to the positive x-axis (that is, 3 o'clock) at time 2.00

2. The distance vector \vec{d}(t) fullfills:
\vec{d}(t)=\vec{r}_{hour}(t)-\vec{r}_{min}(t)
The distance, d(t) fullfills:
d(t)=||\vec{d}(t)|| that is, the LENGTH of the distance vector.
3. The separation velocity is therefore given as:
\frac{dd}{dt}

[KataKoniK]

Thanks for your hlep