PROJECTILE MOTION

PROJECTILE
•                       Projectile is the name given to a body thrown with some initial velocity, and then allowed to move in two dimensions under the action of gravity alone, without being propelled by any engine or fuel. The path followed by a projectile is called its trajectory.
Examples of projectiles
•       A cricket ball hit by a bat.
•       A javelin or hammer thrown by an athlete.

•       A bullet fired from a rifle.
•       A piece of stone thrown in any direction.

ASSUMPTIONS IN PROJECTILE MOTION

There is no frictional resistance of air.
•       The effect due to rotation of earth and curvature of the earth is negligible.
•       The acceleration due to gravity is constant in magnitude and direction at all points of the motion of projectile.

ANGULAR PROJECTION
•       OX,is a horizontal line on ground and
•        OY is a vertical line perpendicular to ground.
•        Suppose a cricket ball be projected from the point O with velocity u, making an angle θ  with the horizontal direction OX
Resolving velocity  into two rectangular components, we get
(i) u cosθ , along OX
(ii) u sin θ  along OY.
•        As these two component velocities act at right angles to each other, therefore they are independent of each other.
The horizontal component velocity u cos θ  is constant throughout the motion as there is no accelerating force in the horizontal direction.
The vertical component velocity u sinθ   decreases continuously with height, from O to H, due to downward force of gravity and becomes zero at H.

EQUATION OF TRAJECTORY:

Path of projectile
•       Suppose at any time t, the object reaches at P (x, y) clearly,
•       x= horizontal distance traveled by object in time t
•       y = vertical distance traveled by object in time t.
This is an equation of a parabola

Time of flight

•       . It is the total time for which the object is in flight (i.e. remains in air).  It is denoted by T.
•       The total time of flight consists of two parts
•       Total time of flight = time of ascent + time of descent

Maximum height
It is the maximum vertical height attained by the object above the point of projection during its flight. It is denoted by h.

 Horizontal Range : It is the horizontal distance covered by the object between its point of projection and the point of hitting the ground.  It is denoted by R.
Clearly, the horizontal range is the horizontal distance covered by the object with uniform velocity u cosθ  in the time equal to total time of flight T.

Maximum Horizontal Range

we note that for a given speed u of the object, the value of horizontal range depends upon angle of projection  as g is constant at a place. Therefore horizontal range R will be maximum if
Sin 2θ = maximum = 1
= sin 90°
Or 2θ =90° or θ =45°
This concept has been used by athletes in long jump, javelin throw, cricket ball throw etc

COMMON COLLECTOR CONFIGURATION OF A TRANSISTOR

COMMON COLLECTOR CONNECTION

In  this  configuration  the  input  is  applied  between the  base  and  the  collector and  the  output  is  taken  from  the  collector  and  the  emitter.  Here  the  collector  is common to both the input and the output circuits as shown in Fig.

Common Collector Transistor Circuit

In  common  collector  configuration  the  input  current  is  the  base current  IB  and  the output current is the emitter current IE. The ratio of change in emitter current to the  change in the base current is called current amplification factor.

It is represented by

COMMON COLLECTOR CIRCUIT

A test  circuit  for determining the  static characteristic  of an NPN transistor is shown in Fig. In this circuit the collector is common to both the input and the output circuits.   To   measure   the   base   and   the   emitter   currents,   milli   ammeters   are connected in series with the base and the emitter circuits. Voltmeters are connected   across the input an…