A ball of mass 2kg, charge 1×10^-6 C is dropped from top of a high tower . In space electric field exists in horizontal direction away from the tower whoch vareis as E=(5-2x)×10⁶ V/m. Find the maximum horizontal distance ball can go from the tower and displacement of ball at this instant from the point of projection?

hi ,

 look the figure ,below . it shows only how the horizonta motion occurs

dv/dt = (5-2x)×10⁶   ( 1×10^{-6   )}

  _⁼(5-2x)

dx/dt = v

 dv/dx = (5-2x)/v

v dv = (5-2x) dx

 v^2/ 2]  from 0 to v =  5x - x^2 ]  from o to x

v^2/ 2  =  5x - x^2

 for v =0 ,

 5x - x^2 = 0

 x= 0,  5

so ball will move back at x= 5 , this will be max. horizontal distance

displacement of ball at this instant from the point of projection ,

dx/ dt = v = √ 10x -  2 x^2

    from here we can get time when it reaches  x= 5 ,

in this duration vertical displacement =  1/2 g t ^2

  total  displacement  =  √ ( horiz. displacemen ) ^2 + ( vertical displacement  ) ^2