MTH404 Final Term Notes

Composed by Yaseen Bilal · Dynamics MTH (404) Notes For Final Term Preparation · Lecture (23) · Projectile Motion

Projectile motion is a form of motion where an object moves in a bilaterally

Symmetrical, parabolic path. The path that the object follows is called its

trajectory.

Projectile motion only occurs when there is one force applied at the beginning

on the

Trajectory, after which the only interference is from gravity.

Trajectory of a Projectile

Let a particle of mass ‘m’ is projected from a point ‘O’ with initial velocity ‘vo’

making an angle ‘’ with horizontal. Take ‘O’ as origin and horizontal

and vertical lines through ‘O’ as x-axis and y-axis respectively. ˆ ˆ

ˆ ˆ

ˆ ˆ r xi yj

dr dx dy i j dt dt dt

dx dy v i j dt dt

ˆ

ˆ ˆ ˆ

ˆ ˆ ˆ 0.

0 ,

cos

sin tan sec

cos sin

cos F mg j

F ma

d x d y mg j m i j dt dt

d x d y i g j i j dt dt

d x d y g dt dt

d x dx A dt dt

d y dy gt B dt dt

dx t V dt

dy gx V y x dt V

A V B V

dx dy V gt V dt dt sin cos

sin

cos cos

sin sin cos

cos x V t

y V gt

x x V C t V

t x y V t g D y V V

x t x y g V

c D

Definition:

Trajectory is the path described by any projectile.

Lecture (24)

Properties of projectile

Objects experiencing projectile motion have a constant velocity in the

horizontal direction, and a constantly changing velocity in the vertical

direction. The trajectory resulting from this combination always has the shape

of parabola.

Notice that the trajectory is a parabola.