A gun is mounted on a trolley which can move uniformly with speed `v m//s` along the `x`-axis. Two shots are find from the origin with the gun making an angle `30^(@)` with the horizontal such that in the first case the trolley is moving along the positive `x`-axis and in the second case moving along the negative `x`- axis. The respective range of the projectile is `250 m` and `200 m`, along the `x-`axis. Find the velocity of the trolley in `m//s`. (Assume height of the trolley to be negligible)(given `g=10m//s^(2)`).

Explanation

To solve the problem step by step, we will use the principles of projectile motion and the effects of the trolley's movement on the projectile's range.

### Step 1: Understand the Problem
We have a gun mounted on a trolley that can move along the x-axis. The gun fires at an angle of 30 degrees to the horizontal. The trolley moves in two different directions, and we need to find its speed based on the ranges of the projectile.

### Step 2: Define Variables
- Let \( v \) be the speed of the trolley (in m/s).
- Let \( u \) be the speed of the projectile (in m/s).
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