PROJECTILE MOTION
Projectile
A body which is in flight through the atmosphere but is not being propelled
by any fuel is called projectile.
Assumptions of Projectile Motion
(1) There is no resistance due to air.
(2) The effect due to curvature of earth is negligible.
(3) The effect due to rotation of earth is negligible.
(4) For all points of the trajectory, the acceleration due to gravity ‘g’ is constant in magnitude and direction.
Principles of Physical Independence of Motions
(1) The motion of a projectile is a two-dimensional motion. So, it can be discussed in two parts. Horizontal motion and vertical motion. These two motions take place independent of each other.This is called the principle of physical independence of motions.
(2) The velocity of the particle can be resolved into two mutually perpendicular components. Horizontal component and vertical component.
(3) The horizontal component remains unchanged throughout the flight. The force of gravity continuously affects the vertical component.
(4) The horizontal motion is a uniform motion and the vertical motion is a uniformly accelerated retarded motion.
Types of Projectile Motion
(1) Oblique projectile motion (2) Horizontal projectile motion (3) Projectile
motion on an inclined plane
Oblique Projectile
In projectile motion, horizontal component of velocity (u cos θ), acceleration (g) and mechanical energy remains constant while, speed, velocity, vertical component of velocity (u sin θ), momentum kinetic energy and potential energy all changes. Velocity, and KE are maximum at
the point of projection while minimum (but not zero) at highest point.
Equation of trajectory : A projectile thrown with velocity u at an angle
θ with the horizontal. The velocity u can be resolved into two rectangular
components u cos θ component along X-axis and u sin θ component along
Y-axis.
Time of flight : The total time taken by the projectile to go up and come
down to the same level from which it was projected is called time of flight.
For vertical upward motion
Maximum height : It is the maximum height from the point of projection, a projectile can reach
Horizontal range : It is the horizontal distance travelled by a body during the time of flight. So by using second equation of motion
Maximum range : A projectile will have maximum range when it is projected at an angle of 45° to the horizontal and the maximum range will be (u2/g). When the range is maximum, the height H reached by the projectile
Motion of a projectile as observed from another projectile is a straight line