A very broad elevator is going up vertically with a constant acceleration of `2m//s^(2)`. At the instant when its velocity is `4m//s` a ball is projected form the floor of the lift with a speed of `4m//s` relative to the floor at an elevation of `30^(@)`. Time taken by the ball to return the floor is `(g=10ms^(2))`

Options

A. `2 sqrt(3) m`
B. `sqrt(3) m`
C. `(2)/(sqrt(3)) m`
D. `2m`

Explanation

To solve the problem step by step, we will analyze the motion of the ball projected from the elevator.

### Step 1: Understand the situation
The elevator is moving upward with a constant acceleration of \(2 \, \text{m/s}^2\) and has a velocity of \(4 \, \text{m/s}\) at the moment the ball is projected. The ball is projected at an angle of \(30^\circ\) with a speed of \(4 \, \text{m/s}\) relative to the elevator's floor.

### Step 2: Determine the effective acceleration of the ball
The ball experiences two accelerations:
1. The gravitational acceleration \(g = 10 \, \text{m/s}^2\) acting downward.
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