The average value of the projectile height y over the horizontal interval 0≤x≤R is:
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The average value of the projectile height y over the horizontal interval 0≤x≤R is:

G1 Physics · Accepted Answer

The average value of y over 0≤x≤R is average height = (1/R)∫₀ᴿ y dx. But ∫₀ᴿ y dx = area under the trajectory = 2RH/3. Therefore average height = 2H/3.