Page 41 - Electrostatics-11

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1 2
= ( )
2

2
, = ( )
2 2

This is the required equation of path. It shows that the path followed by a projectile
is parabolic in nature.

Velocity at any instant:

Let P be the position of projectile at any time t. The velocity v at the point P can
be resolved into two mutually perpendicular directions.

Horizontal component =

Vertical component =

For horizontal motion, = =

For vertical motion, u = 0, a = g

= + =

Now, the resultant velocity is

2
, = √ + = √ + ( ) = √ +
2
2
2
2 2
2

It gives the magnitude of resultant.
Let be the angle made by the resultant with horizontal.

From figure, = =

= −1 ( )

It gives the direction of resultant.

Time of flight (T):

For vertical motion, = 0, = , = ℎ, = =?

18 Mechanics