Show that motion of a charged particle when it is projected at right angles to a uniform electric field is parabolic.

Explanation

Let m is mass of charge particle q is charge on the particle.

E is a uniform electric field.
`u_(x)= u rArr u_(y)= 0`
Initially, along X-axis,
`t= (x)/(u_(x))= (x)/(u) and m a= qE [ because a = (qE)/(m)]`
Along Y-axis,
`y= u_(y)+ (1)/(2) a t^(2) = 0 + (1)/(2) ((qE)/(m)) ((x)/(u))^(2)`
`rArr y= ((qE)/(2m u^(2)))x^(2)`
`rArr y prop x^(2)`
This relation show that path is parabolic