Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_131

2/131 At time \( t = 0 \), the baseball player releases a ball with the initial conditions shown in the figure. Determine the quantities \( r, \dot{r}, \ddot{r}, \theta, \dot{\theta} \), and \( \ddot{\theta} \), all relative to the \( x \)-\( y \) coordinate system shown, at time \( t = 0.5 \) sec. Given from Figure: Initial speed: \( v_0 = 100 \text{ ft/sec} \) Launch angle: \( \alpha = 30^\circ \) Initial position: \( x_0 = 0 \), \( y_0 = 6 \text{ ft} \) Origin \( O \) is at the feet of the player.