A charged ball of mass m and charge q is projected from the ground with an initail velocity u and angle of projection `theta` at the time of projection vertically upward electric field E is switched on. When it reaches the maximum height electric filed is switched off and a horizontal electric feild of same magnitude E is switched on. Then answer the following question (Assume mg> qE)
Q In the above experiment

Options

A. horizionatl velocity always remains constant
B. horizontal velocity remains constant for half of the time and then varies.
C. horizontal velocity when it strikes the grounds is greater than the intial horizontal velocity
D. the initial vertical speed is equal to the final vertical speede.

Answer

To solve the problem step by step, we will analyze the motion of the charged ball under the influence of the electric field and gravity.

### Step 1: Analyze the Initial Conditions
The ball is projected with an initial velocity \( u \) at an angle \( \theta \). The initial horizontal and vertical components of the velocity can be expressed as:
- Horizontal component: \( u_x = u \cos \theta \)
- Vertical component: \( u_y = u \sin \theta \)