more tweaks to SIM_cannon_analytic doc ans images

trick_sims/SIM_cannon_analytic/README.md

@@ -8,7 +8,7 @@ Here we simulate the flight of a cannon ball. We want to know the position and v
 velocity, and subject to the following assumptions and limitations:
 
 * The **only** force acting on the cannon ball is gravity.
-* The acceleration of gravity (g) is constant and equal to -9.81 meters per
+* The acceleration of gravity (g) is **constant** and equal to -9.81 meters per
   second squared.
 * The surface of the ground is defined as where y=0.
 
@@ -18,18 +18,29 @@ velocity, and subject to the following assumptions and limitations:
 
 This problem has a closed-form solution, so that's what is used.
 
-![v_{x0}=S\cos\theta](images/init_v_x_0.png)
+<!--
+Tex: v_{x0}=S\cos\theta
+-->
+![](images/init_v_x_0.png)
 
-![v_{y0}=S\sin\theta](images/init_v_y_0.png)
+<!--
+Tex: v_{y0}=S\sin\theta
+-->
+![](images/init_v_y_0.png)
+
+![](images/init_a_x.png)
+
+![](images/init_a_y.png)
 
 ![](images/solution_vx.png)
 
-![](images/solution_vy.png)
+![v_{y}(t) = gt +v_{y0}](images/solution_vy.png)
 
 ![](images/solution_x.png)
 
 ![](images/solution_y.png)
 
+
 The cannon ball will impact the ground, when y(t)=0 at:
 
 ![](images/time_of_impact.png)
@@ -40,8 +51,8 @@ Model Variable                              | Simulation Variable | Type    | Un
 --------------------------------------------|---------------------|---------|-------
 ![](images/x_0.png), ![](images/y_0.png)    | CANNON.pos0[2]      |double[2]| m
 ![](images/v_x_0.png), ![](images/v_y_0.png)| CANNON.vel0[2]      |double[2]| m/s
-![\theta](images/param_theta.png)           | CANNON.init\_angle   |double   | r
-![speed](images/param_s.png)                | CANNON.init\_speed   |double   | m/s
+![\theta](images/param_theta.png)           | CANNON.init\_angle  |double   | r
+![speed](images/param_s.png)                | CANNON.init\_speed  |double   | m/s
 ![\vec{x}](images/vector_x.png)             | CANNON.pos[2]       |double[2]| m
 ![\vec{v}](images/vector_v.png)             | CANNON.vel[2]       |double[2]| m/s