Normal and Tangential Acceleration

[aaronfue]

Homework Statement

A motorcyclist travels around a curved path that has a radius of 450 ft. While traveling around the curved path, the motorcyclist increases speed by 1.10$\frac{ft}{s}$. Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.00 $\frac{ft}{s^2}$

Homework Equations

a = √(a_t)²+(a_n)²

a_t=$\dot{v}$
a_n = $\frac{v^2}{ρ}$

The Attempt at a Solution

I've already solved for the speed at a given acceleration, and the magnitude of the acceleration at a given speed.

But this part is a little confusing for me. I am thinking that I have to use the equation a = √(a_t)²+(a_n)² and set a = 7.00 $\frac{ft}{s^2}$ and then I can solve for a_n...then solve for v in the equation a_n = $\frac{v^2}{ρ}$, where ρ = 450 ft? But I'm not sure. I will give it a try, though.

If anyone can weigh in on my approach, I would greatly appreciate it as always!

 

[Simon Bridge]

That's how I'd interpret the problem - the total acceleration would be the vector sum of the tangential and centripetal accelerations.

 

[aaronfue]

That's how I'd interpret the problem - the total acceleration would be the vector sum of the tangential and centripetal accelerations.

Thanks. Worked out fine.