If at point of projection , the velcoity of particle is "u" and is direction at an angle `alpha` to the horizontal , then show that it will be moving at right angles to the its initial direction after a time `((u "cosec" alpha))/(g)`

Explanation

To solve the problem, we need to show that a particle projected with an initial velocity \( u \) at an angle \( \alpha \) to the horizontal will be moving at right angles to its initial direction after a time \( t = \frac{u \csc \alpha}{g} \).

### Step-by-Step Solution:

1. **Resolve the Initial Velocity**:
The initial velocity \( u \) can be resolved into two components:
- Horizontal component:
\[
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