Trajectory Formula

The trajectory of a projectile can be described by the equations of motion. The basic formula for the trajectory of a projectile which is launched at some angle 𝚹 from the ground level with an initial velocity is,

has parametric equations:

1. Horizontal motion

2. Vertical motion

As, 

x(t)= Horizontal position at time t

y(t)= Vertical position at time t

G is the gravitational  acceleration

t= time in second

Trajectory Equation

The trajectory can be written as one equation (removing \

t), by solving for t from the horizontal motion equation

Substitute this into the vertical motion equation

This is a parabolic equation, and is the trajectory of the projectile.

The maximum height H can be found from

The range R (horizontal distance travelled when it hits the ground) can be found as

It assumes no air resistance and that the launch and landing heights are equal.

Solved questions

Q1: Maximum Height

Known:

Initial velocity, 

Launch angle, 

Find:

Maximum height reached by the projectile.

Solution

Compute the vertical component of velocity

Applying maximum height formula

Q1:Range of the Projectile

Given:

Initial velocity, 

Launch angle, 

Solution

Range  formula 

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