Constrained to move Horizontally

Sheen91

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



2. Relevant equations

v = [tex]\dot{r}[/tex] [tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex] [tex]\hat{\vartheta}[/tex]

3. The attempt at a solution

[tex]\dot{r}[/tex] = ?
\vartheta = 80°
v = 55mm/s

So I guess I just use the formula above.

v = [tex]\dot{r}[/tex] [tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex] [tex]\hat{\vartheta}[/tex]

55² = [tex]\dot{r}[/tex]² + rΘ'

And so you try and solve for [tex]\dot{r}[/tex]

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

lanedance

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

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

Sheen91

I manage to get the question.

Thanks :D