Forest UCM PnCP ProjMotion - Revision history

Foretony: /* Friction depends linearly on velocity */

2021-09-07T14:27:14Z

Friction depends linearly on velocity

2021-09-07T14:23:36Z

Friction depends linearly on velocity

2014-09-01T15:14:06Z

Taylor expand ln term in Range equation

2014-09-01T15:13:53Z

Taylor expand ln term in Range equation

2014-09-01T15:13:12Z

Taylor expand ln term in Range equation

2014-09-01T15:12:10Z

Taylor expand ln term in Range equation

2014-09-01T15:11:52Z

Taylor expand ln term in Range equation

2014-09-01T15:10:44Z

Taylor expand ln term in Range equation

2014-09-01T15:09:02Z

Taylor expand ln term in Range equation

2014-09-01T15:07:34Z

Taylor expand ln term in Range equation

← Older revision		Revision as of 14:27, 7 September 2021
Line 37:		Line 37:
	:<math>y = -v_t t + \frac{m}{b}\left ( v_{iy} + v_t \right ) \left ( 1- e^{-\frac{b}{m}t} \right ) </math>		:<math>y = -v_t t + \frac{m}{b}\left ( v_{iy} + v_t \right ) \left ( 1- e^{-\frac{b}{m}t} \right ) </math>

−	where <math>v_{iy}</math> has ~~replced~~ <math>v_0</math> so the components are more explicitly identifiable.	+	where <math>v_{iy}</math> has replaced <math>v_0</math> so the components are more explicitly identifiable.

@@ Line 15: / Line 15: @@
 : <math>x=  \frac{m}{b} v_{ix} \left ( 1-e^{-\frac{b}{m}t} \right )</math>
-where <math>v_{ix}</math> has replced <math>v_i</math> so the components are more explicitly identifiable.
+where <math>v_{ix}</math> has replaced <math>v_i</math> so the components are more explicitly identifiable.
 in the y-direction however, the directions are changed to represent an object moving upwards instead of falling

@@ Line 148: / Line 148: @@
 :<math>  R  \sim \frac{2v_{iy}v_{ix} \tau}{v_t}    -  \frac{2 R^2 v_{ix} \tau}{3 v_{ix}^2 \tau^2}  </math>
 ::<math>   \sim \frac{2v_{iy}v_{ix}}{g}    -  \frac{2 }{3 v_{ix} \tau} R^2 </math>
-::<math>   \sim \R_{vacuum}    -  \frac{2 }{3 v_{ix} \tau} R^2 </math>
+::<math>   \sim R_{vacuum}    -  \frac{2 }{3 v_{ix} \tau} R^2 </math>
 [[Forest_UCM_PnCP#Projecile_Motion]]

@@ Line 147: / Line 147: @@
 :<math>  \frac{R }{2v_{ix} \tau} \sim \frac{v_{iy}}{v_t}    -  \frac{R^2 }{3 v_{ix}^2 \tau^2}  </math>
 :<math>  R  \sim \frac{2v_{iy}v_{ix} \tau}{v_t}    -  \frac{2 R^2 v_{ix} \tau}{3 v_{ix}^2 \tau^2}  </math>
-:: :<math>   \sim \frac{2v_{iy}v_{ix}}{g}    -  \frac{2 R^2 }{3 v_{ix} \tau}  </math>
+::<math>   \sim \frac{2v_{iy}v_{ix}}{g}    -  \frac{2 }{3 v_{ix} \tau} R^2 </math>
 [[Forest_UCM_PnCP#Projecile_Motion]]

@@ Line 147: / Line 147: @@
 :<math>  \frac{R }{2v_{ix} \tau} \sim \frac{v_{iy}}{v_t}    -  \frac{R^2 }{3 v_{ix}^2 \tau^2}  </math>
 :<math>  R  \sim \frac{2v_{iy}v_{ix} \tau}{v_t}    -  \frac{2 R^2 v_{ix} \tau}{3 v_{ix}^2 \tau^2}  </math>
 [[Forest_UCM_PnCP#Projecile_Motion]]

@@ Line 145: / Line 145: @@
 :<math> v_{iy}   =  v_t\left ( \frac{R }{2v_{ix} \tau}+ \frac{R^2 }{3 v_{ix}^2 \tau^2}  + \cdots \right )</math>
-:<math>  \frac{R }{2v_{ix} \tau} =\frac{v_{iy}}{v_t}    -  \frac{R^2 }{3 v_{ix}^2 \tau^2}  </math>
+:<math>  \frac{R }{2v_{ix} \tau} \sim \frac{v_{iy}}{v_t}    -  \frac{R^2 }{3 v_{ix}^2 \tau^2}  </math>
 [[Forest_UCM_PnCP#Projecile_Motion]]

@@ Line 143: / Line 143: @@
 :<math> \frac{  v_{iy} + v_t }{v_{ix}}  = v_t \tau \left ( \frac{1 }{v_{ix} \tau} + \frac{R }{2v_{ix}^2 \tau^2}+ \frac{R^2 }{3 v_{ix}^3 \tau^3}  + \cdots \right )</math>
 :<math> v_{iy} + v_t   = v_t \left ( 1  + \frac{R }{2v_{ix} \tau}+ \frac{R^2 }{3 v_{ix}^2 \tau^2}  + \cdots \right )</math>
 [[Forest_UCM_PnCP#Projecile_Motion]]

← Older revision		Revision as of 15:07, 1 September 2014
Line 142:		Line 142:

	:<math> \frac{ v_{iy} + v_t }{v_{ix}} = v_t \tau \left ( \frac{1 }{v_{ix} \tau} + \frac{R }{2v_{ix}^2 \tau^2}+ \frac{R^2 }{3 v_{ix}^3 \tau^3} + \cdots \right )</math>		:<math> \frac{ v_{iy} + v_t }{v_{ix}} = v_t \tau \left ( \frac{1 }{v_{ix} \tau} + \frac{R }{2v_{ix}^2 \tau^2}+ \frac{R^2 }{3 v_{ix}^3 \tau^3} + \cdots \right )</math>
		+	:<math> v_{iy} + v_t = v_t \left ( 1 + \frac{R }{2v_{ix} \tau}+ \frac{R^2 }{3 v_{ix}^2 \tau^2} + \cdots \right )</math>

	[[Forest_UCM_PnCP#Projecile_Motion]]		[[Forest_UCM_PnCP#Projecile_Motion]]