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)=urArru_(y)=0`
Initially, along X-axis
`t=(x)/(u_(x))=(x)/(u)` and `ma=qE:.a=(qE)/(m)`
along Y-axis
`y=u_(y)+1/2at^(2)=0+1/2((qE)/(m))(x/y)^(2)`
`rArr" "y((qE)/("2mu"^(2)))x^(2)rArry prop x^(2)`
This relation show the path is parabolic.