Page 43 - Electrostatics-11

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• = along horizontal (a=0)

• = along vertical (a = g)

• The horizontal motion of the projectile is uniform (a = 0) and the vertical
motion is accelerated ( a = g)

Equation of path:

Let P be the position of projectile at any time t. During this time, the projectile has
covered horizontal displacement x and vertical displacement y.

For horizontal motion:

1
2
= +

2
= ( ) … … … ( )

For vertical motion:

1
2
= +

2
1
2
, = ( ) + (− ) … … … ( )
2

Eliminating t from equation ( ) ( )

1 2
= ( ) + (− ) ( )
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 t:

Let P be the position of projectile at any time t. The velocity v at the point P can

be resolved into horizontal component and vertical component as shown in

figure.

For horizontal motion, = =

For vertical motion, = + = + (− ) = −

20 Mechanics