Projectile
Any object that is given an initial velocity obliquely, and that subsequently follows a path determined
by the net constant force, (In this chapter constant force is gravitational force) acting on it is called
a projectile.
We shall consider only trajectories that are of sufficiently short range so that the gravitational
force can be considered constant in both magnitude and direction
The motion of projectile is known as projectile motion.
It is an example of two dimensional motion with constant acceleration
Two perpendicular directions of motion are independent
Consider a projectile thrown with a velocity u making an angle q with the horizontal.
Horizontal range
At the highest point of its trajectory, particle moves horizontally, and hence vertical component of
velocity is zero
Results of article 2.2, and 2.3 are valid only if projectile lands at same horizontal level from
which it was projected.
We get the same range for two angle of projections a and (90 – a) but in both cases,
maximum heights attained by the particles are different
The path followed by a particle (here projectile) during its motion is called its Trajectory. Equation of
trajectory is the relation between instantaneous coordinates (Here x & y coordinate) of the particle.
If we consider the horizontal direction
PROJECTILE THROWN PARALLEL TO THE HORIZONTAL FROM SOME HEIGHT
This is equal to the time taken by the projectile to return to ground. From equation of motion
Distance covered by the projectile along the horizontal direction between the point of projection to
the point on the ground
Here horizontal velocity of the projectile after time t
Velocity with which the projectile hits the ground
The path traced by projectile is called the trajectory
Case (i) : Horizontal projection
When a ball is thrown upward from a truck moving with uniform speed, then observer A standing in
the truck, will see the ball moving in straight vertical line (upward & downward).
The observer B sitting on road, will see the ball moving in a parabolic path. The horizontal speed of
the ball is equal to the speed of the truck
Case (i) : Particle is projected up the incline
Here a is angle of projection w.r.t. the inclined plane.
x and y axis are taken along and perpendicular to the
incline as shown in the diagram.
When the particle strikes the inclined plane x coordinate is equal to range of the particle
Suppose a projectile is projected with speed u at an angle q from point O on the ground. Range of the projectile
is R. A vertical, smooth wall is present in the path of the projectile at a distance x from the point O. The collision
of the projectile with the wall is elastic. Due to collision, direction of x component of velocity is reversed but its
magnitude remains the same and y component of velocity remains unchanged.
This gives the work done by the net force during a displacement S
of the particle.
We can rewrite equation
A force is said to be non-conservative if work done by or against the force in moving a body depends upon the
path between the initial and final positions.
