A trajectory or flight path in physics is defined as the path that an object in motion having some mass follows through space as a function of time. Hamiltonian mechanics via canonical coordinates is used to define the trajectory of an object in classical mechanics. Hence both position and momentum simultaneously define a complete trajectory. For example, the motion of a ball or a big rock thrown upwards or the motion of a satellite or a bullet fired from a gun .
Derivation of Equation of Trajectory
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The equation of trajectory derivation is as follows ---
y= x tanϴ - (gx2/2 v2 cos2ϴ)
where, ‘x’ is the horizontal component of the trajectory.
‘y’ is the vertical component of the trajectory.
‘g’ is the gravitational force of attraction.
‘v’ is the initial velocity of the object.
‘ϴ’ is the angle of elevation of the trajectory.
Some Important Trajectory Related Equations are as Follows
Time of Flight, T = (2 vo sinϴ/g)
Maximum Height Reached, H =( v02 sin2ϴ/ 2g )
Horizontal Range , R = (vo2 sin2ϴ/ g)
Where , ‘vo’ is the initial velocity
‘sinϴ’ is the vertical component of y-axis
‘cosϴ’ is the horizontal component of x-axis.
Thus the trajectory equation along with some important formulae has been derived.
Objects will follow a vertically symmetric path when projected from and land on the same horizontal surface. The flight time depends on the initial velocity of the projectile and the angle of projection. The maximum height of the projectile is reached when the velocity of the object is zero.The range of the projectile depends on the initial velocity of the object.
This article explains the trajectory formula and the derivation of the equation of trajectory. Some FAQs have been added for a better understanding of the topic for the students.