(Solved): Centripetal and Tangential Acceleration A snowboarder slides down a curved ramp of radius r. At so ...

Centripetal and Tangential Acceleration A snowboarder slides down a curved ramp of radius $$r$$. At some instant he is traveling at speed $$v$$ and his speed is increasing at a rate $$a_t$$. The angle between his acceleration and velocity vectors is $$?$$. Solution: Formula for centripetal acceleration (which points toward the center of the circular path): $$a_c=\frac{v^2}{r}$$ The acceleration component $$a_t$$ points parallel to velocity (that is, tangent to the circular path). The acceleration component $$a_c$$ points perpendicular to velocity. So we can apply right triangle vector trig: $$\tan ?=\frac{\text{ opposite }}{\text{ adjacent }}=\frac{a_c}{a_t}$$ Plug in for $$a_c$$ : $$\tan ?=\frac{v^2}{r{a}_t}$$