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Trajectory of a Projectile

Trajectory of a projectile is the curved path given an initial velocity and is acted on by gravity.  The projectile is acted upon by both vertical and horizontal motion along the trajectory.

trajectory angle 1

Trajectory of a Projectile formula

y=dtanθ(gd2/2v20cos2(θ)) 
Symbol English Metric
y = vertical position ft deg
θ = angle of the initial vertical from x-axis deg rad
g = gravitational acceleration ft/sec2 m/s2
d = horizontal position ft m
v0 = launch velocity ft/sec m/s

     

trajectory range 1

horizontal range of a Projectile formula

R=v20sin2(θ)/g 
Symbol English Metric
R = horizontal range ft  m
v0 = launch velocity ft/sec  m/s 
θ = vertical angle deg rad
g = gravitational acceleration  ft/sec2   m/s2   

    

trajectory range 1

Launch Velocity of a Projectile formula

v0=Rg/sin2(θ) 
Symbol English Metric
v0 = launch velocity ft/sec m/s
R = horizontal range ft m
g = gravitational acceleration ft/sec2 m/s2
θ = vertical angle deg rad

      

trajectory max height

Maximum Height of a Projectile formula

hmax=v0sin2(θ)/2g 
Symbol English Metric
hmax = maximum height ft m
v0 = launch velocity ft/sec m/s
θ = vertical angle deg rad
g = gravitational acceleration ft/sec2 m/s2

    

trajectory clearing 1

Projectile Clearing an Object formula

yh=(dv0y/v0x)[12g(x2/v20x)] 
Symbol English Metric
yh = vertical position ft m 
d = horizontal position ft m
v0 = launch velocity ft/sec m/s
g = gravitational acceleration ft/sec2 m/s2
θ = angle of the initial vertical from x-axis deg rad

    

trajectory angle 1

Projectile Launch Angle formula

θ=12sin1(gd/v20) 
Symbol English Metric
θ = angle of the initial vertical from x-axis deg rad
g = gravitational acceleration  ft/sec2   m/s2   
d = horizontal position ft m
v0 = launch velocity ft/sec  m/s 

     

trajectory time

Time of Flight of a Projectile formula

t=2v0sin(θ)/g
Symbol English Metric
t = time sec  s
g = gravitational acceleration  ft/sec2   m/s2   
v0 = launch velocity ft/sec  m/s 
θ = vertical angle deg rad

    

trajectory hill

Trajectory of a Projectile on a Hill formulas

t=(2v0h/g)±(v20h/g2)(2h/g)

d=v0dt 

h=v0ht12gt2 

Symbol English Metric
t = time sec s
g = gravitational acceleration ft/sec2 m/s2
v0 = launch velocity ft/sec m/s
θ = vertical angle rad rad

 

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