Related rates?

  • Thread starter KataKoniK
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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?
 

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

2. The distance vector [tex]\vec{d}(t)[/tex] fullfills:
[tex]\vec{d}(t)=\vec{r}_{hour}(t)-\vec{r}_{min}(t)[/tex]
The distance, d(t) fullfills:
[tex]d(t)=||\vec{d}(t)||[/tex] that is, the LENGTH of the distance vector.
3. The separation velocity is therefore given as:
[tex]\frac{dd}{dt}[/tex]
 
  • #3
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Thanks for your hlep
 

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