Question
Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed u at an angle $\theta$ with the horizontal.

Answer

Total of flight $\text{T}=\frac{2\text{u}\sin\theta}{\text{g}}$
Average velocity $=\frac{\text{change in displacement}}{\text{time}}$
From the figure, it can be said AB is horizontal. So there is no effect of vertical component of the velocity during this displacement.
So because the body moves at a constant speed of $'\text{u}\cos\theta'$ in horizontal direction.
The average velocity during this displacement will be $\text{u}\cos\theta$ in the horizontal direction.

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