# Homework Help: Constrained to move Horizontally

1. Aug 8, 2010

### Sheen91

1. The problem statement, all variables and given/known data

[PLAIN]http://img231.imageshack.us/img231/636/question2m.jpg [Broken]

2. Relevant equations

v = $$\dot{r}$$ $$\hat{r}$$ + r$$\dot{\vartheta}$$ $$\hat{\vartheta}$$

3. The attempt at a solution

$$\dot{r}$$ = ?
\vartheta = 80°
v = 55mm/s

So I guess I just use the formula above.

v = $$\dot{r}$$ $$\hat{r}$$ + r$$\dot{\vartheta}$$ $$\hat{\vartheta}$$

55² = $$\dot{r}$$² + rΘ'

And so you try and solve for $$\dot{r}$$

r'² = 55² - (r*Θ')²
r' = sqrt(55² - (r*Θ')²)

And then I get stuck. I am either missing something. Or not doing something right. I guess this isn't really r theta, it is more a conversion from r theta to x-y.

Not 100% sure how to do that though.

Cheers

Last edited by a moderator: May 4, 2017
2. Aug 8, 2010

### lanedance

first you can write sevreal expresisons in tex as follows
$$\vec{v} = \dot{r} \hat{r} + r \dot{\vartheta}\hat{\vartheta}$$

so knowing theta and |v| you should be able to decompose v into components in the orthogonal directions $\hat{r}, \hat{\vartheta}$

3. Aug 11, 2010

### Sheen91

I manage to get the question.

Thanks :D