A particle is projected with a velocity of `10sqrt2 m//s` at an angle of `45^(@)` with the horizontal. Find the interval between the moments when speed is `sqrt125 m//s(g=10m//s^(2))`

Explanation

To solve the problem, we need to find the time interval between the moments when the speed of a particle projected at an angle is \( \sqrt{125} \, \text{m/s} \). Let's break down the solution step by step.

### Step 1: Identify the Initial Conditions
The particle is projected with an initial velocity \( u = 10\sqrt{2} \, \text{m/s} \) at an angle of \( 45^\circ \) with the horizontal.

### Step 2: Calculate the Components of Initial Velocity
Using trigonometric functions, we can find the horizontal and vertical components of the initial velocity:

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