Two-Dimensional Motion of a Particle: Velocity & Acceleration

[chart2006]

Homework Statement

The two-dimensional motion of a particle is defined by the relationship $$r = \frac {1}{sin\theta - cos\theta}$$ and $$tan\theta = 1 + \frac {1}{t^2}$$, where $$r$$ and $$\theta$$ are expressed in meters and radians, respectively, and $$t$$ is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.

Homework Equations

$$r = \frac {1}{sin\theta - cos\theta}$$


$$tan\theta = 1 + \frac {1}{t^2}$$

The Attempt at a Solution

I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve $$tan\theta$$ for $$\theta$$. Once I've done that I figure I'd need to differentiate both $$r$$ and $$\theta$$ to find $$\dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}$$.

I don't know if I'm on the correct route but any help would be appreciated. thanks!

 

[gabbagabbahey]

I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve $$tan\theta$$ for $$\theta$$.

Tangent is not a one-to-one function, so that's a bad idea.

Instead, draw a picture! I think you can find expressions for $\sin\theta$ and $\cos\theta$ in terms of $t$ without actually solving for $\theta$ first...think 'right triangle'