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 θ with the horizontal.

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Solution

Given:
Initial velocity of the projectile = u
Angle of projection = θ
To find: Average velocity of the projectile
Average velocity $= \frac{Change in displacement}{Time}$
Consider the projectile motion in the figure given below.

By the symmetry of figure, it can be said that the line joining points A and B is horizontal.
So, there will be no effect of the vertical component of velocity of the projectile during displacement AB.
We know that the projectile moves at a constant velocity ucosθ in horizontal direction.
Hence, the average velocity of the projectile is ucosθ.

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