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you could use integration…
the velocity in the x direction is always constant. so the average velocity in the x direction is also the constant velocity with which the body travels i.e u(cos theta)…
but the velocity in the y direction is a little trickier
you have to use the average formula for integration…it goes like this…
lets assume that the velocity in the y direction is a function of y…let that be
velocity in the y direction = f(y)
(i am assuming that the actual function would be easy to find out…using the basic laws of motion )
then integrate the f(y) with the limits from y=0 to y=(maximum height attained by a projectile ) (the formula is easily found on the internet)
after you find out the integral, divide the answer by the maximum height…now you have found the average velocity in the y direction
however you already know the average velocity in the x direction…using them as components find out the average velocity as a total
([velocity in the y direction]^2 + [velocity in the x direction]^2)^(1/2)
i thank that you should get your answer as
({u^2(1+3[cos theta]^2)}^(1/2) )*(1/2)
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