In a region , an electroc field `E = 10NC^(-1)` making an angle of `theta = 30^@` with the horizontal plane is present. Coefficient of restitution between ball and surface is `e = 0.2.` Ball has charge `q = -2C` over it and mass m = 2 kg . Ball is projected at an angle of `theta = 30^@` with the horizontal with speed `u = 10ms^(-1)`

After first impact with the ground,

Options

A. the ball rebounds at an angle `30^@` with the horizontal
B. the ball rebounds at an angle `60^@` with the horizontal
C. the ball rebounds in the vertical direction with velocity `1ms^(-1)`
D. the ball moves in the horizontal direction with velocity `1ms^(-1)`

Answer

C

Explanation

When it hits ground, dispalcement in y-direction will be zero
`5t-(1)/(2)15t^(2)=0` or `t=(2)/(3)s`
At time `t=2//3` s the displacement in x-direction
`x=5sqrt(3)((2)/(3))-(1)/(5)5sqrt(3)((2)/(3))^(2)=(20)/(3sqrt(3))m`
After impact with the surface, velocity along vertical direction
`u'^(y)=eu_(y)=0.2xx5=1ms^(-1)`
velocity along the horizontal direction after time `T_(1)`
`u'_(x)=eu_(x)+a_(x)T_(1)=5sqrt(3)-5sqrt(3)xx(2)/(3)=(5)/(sqrt(3))ms^(-1)`
The ball rebounds in the vertical direction with velocity 1 `ms^(-1)`