A Ballistics Example

 
The following table presents, for different sample firing velocities and angles, the landing distance for a projectile such as a cannon ball. Clicking on a line shows how the calculation was made at prorgessive levels of detail.   »  
The following table presents, for different sample firing velocities and angles, the landing distance for a projectile such as a cannon ball. Clicking on a line shows how the calculation was made at prorgessive levels of detail.

 
 Velocity  Angle    Distance   Calculation
 
   50 m/s  10 °     0.0873 km  calculated distance travelled
   50 m/s  20 °     0.1640 km  calculated distance travelled
   50 m/s  30 °     0.2209 km  calculated distance travelled
   50 m/s  40 °     0.2512 km  calculated distance travelled
   50 m/s  50 °     0.2512 km  calculated distance travelled
   50 m/s  60 °     0.2209 km  calculated distance travelled
   50 m/s  70 °     0.1640 km  calculated distance travelled
   50 m/s  80 °     0.0873 km  calculated distance travelled
  200 m/s  15 °     2.0408 km  calculated distance travelled
1,000 m/s  45 °   102.0408 km  calculated distance travelled
2,000 m/s  60 °   353.4798 km  calculated distance travelled
50 m/s  10 °  0.0873 km  calculated distance travelled

 
  49.2404 m/s  lateral speed ( velocity = 50 m/s, angle = 10 ° )
×  1.7719 s    time in the air ( velocity = 50 m/s, angle = 10 ° )
 
=  0.0873 km   Distance
 
49.2404 m/s  lateral speed ( velocity = 50 m/s, angle = 10 ° )

 
  50      m/s  sample[velocity]
×  0.9848      lateral component
 
0.9848  lateral component

 
      0.1745 °rad  angle from horizontal in radians
cos = 0.9848       
 
0.1745 °rad  angle from horizontal in radians

 
   10      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
1.7719 s  time in the air ( velocity = 50 m/s, angle = 10 ° )

 
  8.6824 m/s   vertical speed
× 2            
÷ 9.8000 m/s²  gravitatonal velocity
 
8.6824 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.1736      vertical component
 
0.1736  vertical component

 
      0.1745 °rad  angle from horizontal in radians
sin = 0.1736       
 
0.1745 °rad  angle from horizontal in radians

 
   10      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  20 °  0.1640 km  calculated distance travelled

 
  46.9846 m/s  lateral speed ( velocity = 50 m/s, angle = 20 ° )
×  3.4900 s    time in the air ( velocity = 50 m/s, angle = 20 ° )
 
=  0.1640 km   Distance
 
46.9846 m/s  lateral speed ( velocity = 50 m/s, angle = 20 ° )

 
  50      m/s  sample[velocity]
×  0.9397      lateral component
 
0.9397  lateral component

 
      0.3491 °rad  angle from horizontal in radians
cos = 0.9397       
 
0.3491 °rad  angle from horizontal in radians

 
   20      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
3.4900 s  time in the air ( velocity = 50 m/s, angle = 20 ° )

 
  17.1010 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
17.1010 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.3420      vertical component
 
0.3420  vertical component

 
      0.3491 °rad  angle from horizontal in radians
sin = 0.3420       
 
0.3491 °rad  angle from horizontal in radians

 
   20      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  30 °  0.2209 km  calculated distance travelled

 
  43.3013 m/s  lateral speed ( velocity = 50 m/s, angle = 30 ° )
×  5.1020 s    time in the air ( velocity = 50 m/s, angle = 30 ° )
 
=  0.2209 km   Distance
 
43.3013 m/s  lateral speed ( velocity = 50 m/s, angle = 30 ° )

 
  50      m/s  sample[velocity]
×  0.8660      lateral component
 
0.8660  lateral component

 
      0.5236 °rad  angle from horizontal in radians
cos = 0.8660       
 
0.5236 °rad  angle from horizontal in radians

 
   30      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
5.1020 s  time in the air ( velocity = 50 m/s, angle = 30 ° )

 
  25      m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
25 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.5000      vertical component
 
0.5000  vertical component

 
      0.5236 °rad  angle from horizontal in radians
sin = 0.5000       
 
0.5236 °rad  angle from horizontal in radians

 
   30      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  40 °  0.2512 km  calculated distance travelled

 
  38.3022 m/s  lateral speed ( velocity = 50 m/s, angle = 40 ° )
×  6.5591 s    time in the air ( velocity = 50 m/s, angle = 40 ° )
 
=  0.2512 km   Distance
 
38.3022 m/s  lateral speed ( velocity = 50 m/s, angle = 40 ° )

 
  50      m/s  sample[velocity]
×  0.7660      lateral component
 
0.7660  lateral component

 
      0.6981 °rad  angle from horizontal in radians
cos = 0.7660       
 
0.6981 °rad  angle from horizontal in radians

 
   40      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
6.5591 s  time in the air ( velocity = 50 m/s, angle = 40 ° )

 
  32.1394 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
32.1394 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.6428      vertical component
 
0.6428  vertical component

 
      0.6981 °rad  angle from horizontal in radians
sin = 0.6428       
 
0.6981 °rad  angle from horizontal in radians

 
   40      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  50 °  0.2512 km  calculated distance travelled

 
  32.1394 m/s  lateral speed ( velocity = 50 m/s, angle = 50 ° )
×  7.8168 s    time in the air ( velocity = 50 m/s, angle = 50 ° )
 
=  0.2512 km   Distance
 
32.1394 m/s  lateral speed ( velocity = 50 m/s, angle = 50 ° )

 
  50      m/s  sample[velocity]
×  0.6428      lateral component
 
0.6428  lateral component

 
      0.8727 °rad  angle from horizontal in radians
cos = 0.6428       
 
0.8727 °rad  angle from horizontal in radians

 
   50      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
7.8168 s  time in the air ( velocity = 50 m/s, angle = 50 ° )

 
  38.3022 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
38.3022 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.7660      vertical component
 
0.7660  vertical component

 
      0.8727 °rad  angle from horizontal in radians
sin = 0.7660       
 
0.8727 °rad  angle from horizontal in radians

 
   50      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  60 °  0.2209 km  calculated distance travelled

 
  25      m/s  lateral speed ( velocity = 50 m/s, angle = 60 ° )
×  8.8370 s    time in the air ( velocity = 50 m/s, angle = 60 ° )
 
=  0.2209 km   Distance
 
25 m/s  lateral speed ( velocity = 50 m/s, angle = 60 ° )

 
  50      m/s  sample[velocity]
×  0.5000      lateral component
 
0.5000  lateral component

 
      1.0472 °rad  angle from horizontal in radians
cos = 0.5000       
 
1.0472 °rad  angle from horizontal in radians

 
   60      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
8.8370 s  time in the air ( velocity = 50 m/s, angle = 60 ° )

 
  43.3013 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
43.3013 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.8660      vertical component
 
0.8660  vertical component

 
      1.0472 °rad  angle from horizontal in radians
sin = 0.8660       
 
1.0472 °rad  angle from horizontal in radians

 
   60      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  70 °  0.1640 km  calculated distance travelled

 
  17.1010 m/s  lateral speed ( velocity = 50 m/s, angle = 70 ° )
×  9.5887 s    time in the air ( velocity = 50 m/s, angle = 70 ° )
 
=  0.1640 km   Distance
 
17.1010 m/s  lateral speed ( velocity = 50 m/s, angle = 70 ° )

 
  50      m/s  sample[velocity]
×  0.3420      lateral component
 
0.3420  lateral component

 
      1.2217 °rad  angle from horizontal in radians
cos = 0.3420       
 
1.2217 °rad  angle from horizontal in radians

 
   70      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
9.5887 s  time in the air ( velocity = 50 m/s, angle = 70 ° )

 
  46.9846 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
46.9846 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.9397      vertical component
 
0.9397  vertical component

 
      1.2217 °rad  angle from horizontal in radians
sin = 0.9397       
 
1.2217 °rad  angle from horizontal in radians

 
   70      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
50 m/s  80 °  0.0873 km  calculated distance travelled

 
   8.6824 m/s  lateral speed ( velocity = 50 m/s, angle = 80 ° )
× 10.0491 s    time in the air ( velocity = 50 m/s, angle = 80 ° )
 
=  0.0873 km   Distance
 
8.6824 m/s  lateral speed ( velocity = 50 m/s, angle = 80 ° )

 
  50      m/s  sample[velocity]
×  0.1736      lateral component
 
0.1736  lateral component

 
      1.3963 °rad  angle from horizontal in radians
cos = 0.1736       
 
1.3963 °rad  angle from horizontal in radians

 
   80      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
10.0491 s  time in the air ( velocity = 50 m/s, angle = 80 ° )

 
  49.2404 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
49.2404 m/s  vertical speed

 
  50      m/s  sample[velocity]
×  0.9848      vertical component
 
0.9848  vertical component

 
      1.3963 °rad  angle from horizontal in radians
sin = 0.9848       
 
1.3963 °rad  angle from horizontal in radians

 
   80      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
200 m/s  15 °  2.0408 km  calculated distance travelled

 
  193.1852 m/s  lateral speed ( velocity = 200 m/s, angle = 15 ° )
×  10.5640 s    time in the air ( velocity = 200 m/s, angle = 15 ° )
 
=   2.0408 km   Distance
 
193.1852 m/s  lateral speed ( velocity = 200 m/s, angle = 15 ° )

 
  200      m/s  sample[velocity]
×   0.9659      lateral component
 
0.9659  lateral component

 
      0.2618 °rad  angle from horizontal in radians
cos = 0.9659       
 
0.2618 °rad  angle from horizontal in radians

 
   15      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
10.5640 s  time in the air ( velocity = 200 m/s, angle = 15 ° )

 
  51.7638 m/s   vertical speed
×  2            
÷  9.8000 m/s²  gravitatonal velocity
 
51.7638 m/s  vertical speed

 
  200      m/s  sample[velocity]
×   0.2588      vertical component
 
0.2588  vertical component

 
      0.2618 °rad  angle from horizontal in radians
sin = 0.2588       
 
0.2618 °rad  angle from horizontal in radians

 
   15      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
1,000 m/s  45 °  102.0408 km  calculated distance travelled

 
  707.1068 m/s  lateral speed ( velocity = 1,000 m/s, angle = 45 ° )
× 144.3075 s    time in the air ( velocity = 1,000 m/s, angle = 45 ° )
 
= 102.0408 km   Distance
 
707.1068 m/s  lateral speed ( velocity = 1,000 m/s, angle = 45 ° )

 
  1,000      m/s  sample[velocity]
×     0.7071      lateral component
 
0.7071  lateral component

 
      0.7854 °rad  angle from horizontal in radians
cos = 0.7071       
 
0.7854 °rad  angle from horizontal in radians

 
   45      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
144.3075 s  time in the air ( velocity = 1,000 m/s, angle = 45 ° )

 
  707.1068 m/s   vertical speed
×   2            
÷   9.8000 m/s²  gravitatonal velocity
 
707.1068 m/s  vertical speed

 
  1,000      m/s  sample[velocity]
×     0.7071      vertical component
 
0.7071  vertical component

 
      0.7854 °rad  angle from horizontal in radians
sin = 0.7071       
 
0.7854 °rad  angle from horizontal in radians

 
   45      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
2,000 m/s  60 °  353.4798 km  calculated distance travelled

 
  1,000      m/s  lateral speed ( velocity = 2,000 m/s, angle = 60 ° )
×   353.4798 s    time in the air ( velocity = 2,000 m/s, angle = 60 ° )
 
=   353.4798 km   Distance
 
1,000 m/s  lateral speed ( velocity = 2,000 m/s, angle = 60 ° )

 
  2,000      m/s  sample[velocity]
×     0.5000      lateral component
 
0.5000  lateral component

 
      1.0472 °rad  angle from horizontal in radians
cos = 0.5000       
 
1.0472 °rad  angle from horizontal in radians

 
   60      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
353.4798 s  time in the air ( velocity = 2,000 m/s, angle = 60 ° )

 
  1,732.0508 m/s   vertical speed
×     2            
÷     9.8000 m/s²  gravitatonal velocity
 
1,732.0508 m/s  vertical speed

 
  2,000      m/s  sample[velocity]
×     0.8660      vertical component
 
0.8660  vertical component

 
      1.0472 °rad  angle from horizontal in radians
sin = 0.8660       
 
1.0472 °rad  angle from horizontal in radians

 
   60      °     sample[angle]
÷ 180      °     degrees in half circle
×   3.1416 °rad  radians in half circle
 
 
 

 « The following table presents, for different sample firing velocities and angles, the landing distance for a projectile such as a cannon ball. Clicking on a line shows how the calculation was made at prorgessive levels of detail.
   50      m/s
   10      °  
    0.0873 km 
calculated distance travelled   »  
   50      m/s
   20      °  
    0.1640 km 
calculated distance travelled   »  
   50      m/s
   30      °  
    0.2209 km 
calculated distance travelled   »  
   50      m/s
   40      °  
    0.2512 km 
calculated distance travelled   »  
   50      m/s
   50      °  
    0.2512 km 
calculated distance travelled   »  
   50      m/s
   60      °  
    0.2209 km 
calculated distance travelled   »  
   50      m/s
   70      °  
    0.1640 km 
calculated distance travelled   »  
   50      m/s
   80      °  
    0.0873 km 
calculated distance travelled   »  
  200      m/s
   15      °  
    2.0408 km 
calculated distance travelled   »  
1,000      m/s
   45      °  
  102.0408 km 
calculated distance travelled   »  
2,000      m/s
   60      °  
  353.4798 km 
calculated distance travelled   »  

 « calculated distance travelled
  49.2404 m/s
lateral speed ( velocity = 50 m/s, angle = 10 ° )   »  
×  1.7719 s  
time in the air ( velocity = 50 m/s, angle = 10 ° )   »  
=  0.0873 km 
Distance   

 « calculated distance travelled
  46.9846 m/s
lateral speed ( velocity = 50 m/s, angle = 20 ° )   »  
×  3.4900 s  
time in the air ( velocity = 50 m/s, angle = 20 ° )   »  
=  0.1640 km 
Distance   

 « calculated distance travelled
  43.3013 m/s
lateral speed ( velocity = 50 m/s, angle = 30 ° )   »  
×  5.1020 s  
time in the air ( velocity = 50 m/s, angle = 30 ° )   »  
=  0.2209 km 
Distance   

 « calculated distance travelled
  38.3022 m/s
lateral speed ( velocity = 50 m/s, angle = 40 ° )   »  
×  6.5591 s  
time in the air ( velocity = 50 m/s, angle = 40 ° )   »  
=  0.2512 km 
Distance   

 « calculated distance travelled
  32.1394 m/s
lateral speed ( velocity = 50 m/s, angle = 50 ° )   »  
×  7.8168 s  
time in the air ( velocity = 50 m/s, angle = 50 ° )   »  
=  0.2512 km 
Distance   

 « calculated distance travelled
  25      m/s
lateral speed ( velocity = 50 m/s, angle = 60 ° )   »  
×  8.8370 s  
time in the air ( velocity = 50 m/s, angle = 60 ° )   »  
=  0.2209 km 
Distance   

 « calculated distance travelled
  17.1010 m/s
lateral speed ( velocity = 50 m/s, angle = 70 ° )   »  
×  9.5887 s  
time in the air ( velocity = 50 m/s, angle = 70 ° )   »  
=  0.1640 km 
Distance   

 « calculated distance travelled
   8.6824 m/s
lateral speed ( velocity = 50 m/s, angle = 80 ° )   »  
× 10.0491 s  
time in the air ( velocity = 50 m/s, angle = 80 ° )   »  
=  0.0873 km 
Distance   

 « calculated distance travelled
  193.1852 m/s
lateral speed ( velocity = 200 m/s, angle = 15 ° )   »  
×  10.5640 s  
time in the air ( velocity = 200 m/s, angle = 15 ° )   »  
=   2.0408 km 
Distance   

 « calculated distance travelled
  707.1068 m/s
lateral speed ( velocity = 1,000 m/s, angle = 45 ° )   »  
× 144.3075 s  
time in the air ( velocity = 1,000 m/s, angle = 45 ° )   »  
= 102.0408 km 
Distance   

 « calculated distance travelled
  1,000      m/s
lateral speed ( velocity = 2,000 m/s, angle = 60 ° )   »  
×   353.4798 s  
time in the air ( velocity = 2,000 m/s, angle = 60 ° )   »  
=   353.4798 km 
Distance   

 « lateral speed ( velocity = 50 m/s, angle = 10 ° )
  50      m/s
sample[velocity]   
×  0.9848    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 10 ° )
  8.6824 m/s 
vertical speed   »  
× 2          
   
÷ 9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 20 ° )
  50      m/s
sample[velocity]   
×  0.9397    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 20 ° )
  17.1010 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 30 ° )
  50      m/s
sample[velocity]   
×  0.8660    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 30 ° )
  25      m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 40 ° )
  50      m/s
sample[velocity]   
×  0.7660    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 40 ° )
  32.1394 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 50 ° )
  50      m/s
sample[velocity]   
×  0.6428    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 50 ° )
  38.3022 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 60 ° )
  50      m/s
sample[velocity]   
×  0.5000    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 60 ° )
  43.3013 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 70 ° )
  50      m/s
sample[velocity]   
×  0.3420    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 70 ° )
  46.9846 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 50 m/s, angle = 80 ° )
  50      m/s
sample[velocity]   
×  0.1736    
lateral component   »  

 « time in the air ( velocity = 50 m/s, angle = 80 ° )
  49.2404 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 200 m/s, angle = 15 ° )
  200      m/s
sample[velocity]   
×   0.9659    
lateral component   »  

 « time in the air ( velocity = 200 m/s, angle = 15 ° )
  51.7638 m/s 
vertical speed   »  
×  2          
   
÷  9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 1,000 m/s, angle = 45 ° )
  1,000      m/s
sample[velocity]   
×     0.7071    
lateral component   »  

 « time in the air ( velocity = 1,000 m/s, angle = 45 ° )
  707.1068 m/s 
vertical speed   »  
×   2          
   
÷   9.8000 m/s²
gravitatonal velocity   

 « lateral speed ( velocity = 2,000 m/s, angle = 60 ° )
  2,000      m/s
sample[velocity]   
×     0.5000    
lateral component   »  

 « time in the air ( velocity = 2,000 m/s, angle = 60 ° )
  1,732.0508 m/s 
vertical speed   »  
×     2          
   
÷     9.8000 m/s²
gravitatonal velocity   

 « lateral component
      0.1745 °rad
angle from horizontal in radians   »  
cos = 0.9848     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.1736    
vertical component   »  

 « lateral component
      0.3491 °rad
angle from horizontal in radians   »  
cos = 0.9397     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.3420    
vertical component   »  

 « lateral component
      0.5236 °rad
angle from horizontal in radians   »  
cos = 0.8660     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.5000    
vertical component   »  

 « lateral component
      0.6981 °rad
angle from horizontal in radians   »  
cos = 0.7660     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.6428    
vertical component   »  

 « lateral component
      0.8727 °rad
angle from horizontal in radians   »  
cos = 0.6428     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.7660    
vertical component   »  

 « lateral component
      1.0472 °rad
angle from horizontal in radians   »  
cos = 0.5000     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.8660    
vertical component   »  

 « lateral component
      1.2217 °rad
angle from horizontal in radians   »  
cos = 0.3420     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.9397    
vertical component   »  

 « lateral component
      1.3963 °rad
angle from horizontal in radians   »  
cos = 0.1736     
 

 « vertical speed
  50      m/s
sample[velocity]   
×  0.9848    
vertical component   »  

 « lateral component
      0.2618 °rad
angle from horizontal in radians   »  
cos = 0.9659     
 

 « vertical speed
  200      m/s
sample[velocity]   
×   0.2588    
vertical component   »  

 « lateral component
      0.7854 °rad
angle from horizontal in radians   »  
cos = 0.7071     
 

 « vertical speed
  1,000      m/s
sample[velocity]   
×     0.7071    
vertical component   »  

 « lateral component
      1.0472 °rad
angle from horizontal in radians   »  
cos = 0.5000     
 

 « vertical speed
  2,000      m/s
sample[velocity]   
×     0.8660    
vertical component   »  

 « angle from horizontal in radians
   10      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.1745 °rad
angle from horizontal in radians   »  
sin = 0.1736     
 

 « angle from horizontal in radians
   20      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.3491 °rad
angle from horizontal in radians   »  
sin = 0.3420     
 

 « angle from horizontal in radians
   30      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.5236 °rad
angle from horizontal in radians   »  
sin = 0.5000     
 

 « angle from horizontal in radians
   40      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.6981 °rad
angle from horizontal in radians   »  
sin = 0.6428     
 

 « angle from horizontal in radians
   50      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.8727 °rad
angle from horizontal in radians   »  
sin = 0.7660     
 

 « angle from horizontal in radians
   60      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      1.0472 °rad
angle from horizontal in radians   »  
sin = 0.8660     
 

 « angle from horizontal in radians
   70      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      1.2217 °rad
angle from horizontal in radians   »  
sin = 0.9397     
 

 « angle from horizontal in radians
   80      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      1.3963 °rad
angle from horizontal in radians   »  
sin = 0.9848     
 

 « angle from horizontal in radians
   15      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.2618 °rad
angle from horizontal in radians   »  
sin = 0.2588     
 

 « angle from horizontal in radians
   45      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      0.7854 °rad
angle from horizontal in radians   »  
sin = 0.7071     
 

 « angle from horizontal in radians
   60      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « vertical component
      1.0472 °rad
angle from horizontal in radians   »  
sin = 0.8660     
 

 « angle from horizontal in radians
   10      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   20      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   30      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   40      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   50      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   60      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   70      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   80      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   15      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   45      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

 « angle from horizontal in radians
   60      °   
sample[angle]   
÷ 180      °   
degrees in half circle   
×   3.1416 °rad
radians in half circle   

-> output produced by QuSheet, licenced to "Richard Develyn", 15 Oct 2009 130|1|24094