# Homework help (normal and tangential coordinate problem)

1. Jan 23, 2005

### nineeyes

Problem : A baseball player releases a ball with $$v_0= 100 ft/sec$$ at an angle of $$\theta= 30 degrees$$. Determine the radius of curvature of the trajectory (a) just after release and (b) at the apex. For each case compute the time rate of change of the speed.

I really wasn't sure how to do the problem, so I sort of just guessed at alot of things. So any help would be great. But this is what I did.

I assumed the only acceleration after the ball was thrown was due to gravity.
so I got
$$a_n=-32.2*cos(30)$$ $$a_t=-32.2*sin(30)$$
then I used $$a_n=\frac{v^2}{\rho}$$ to solve for the curvature $$\rho$$ for when the ball was just released I got $$\rho = 358.6 ft$$ . Then I used $$\beta'=\frac{100}{\rho}$$ to solve for the angular rate.

I wasnt sure on how to solve (b) so I just assumed that the angle between $$\theta$$ and the x- axis would be 0 degrees since the apex is the highest point and I guessed that would be when the ball would stop moving up and start going down.

So I got
$$a_n = -32,2 ft/s^2$$
then used
$$a_n=v*\beta'$$ to solve for v at the apex using the the angular rate i got earlier for beta'.
I got $$v=115.4ft/s$$
then using the v and $$a_n$$ I solved for $$\rho$$ using the equation $$a_n=\frac{v^2}{\rho}$$
I got $$\rho= 413 ft$$

I'm definitely not confident with this answer, it's the first time I've done a problem like this, and I'm not sure if everything I did and assumed was legal.
Thanks in advance for any help.