R = 4h

Step 1: Let the greatest height attained by the projectile be denoted as h. The range R is given as R = 2h.
Step 2: The formulas for the range R and the maximum height h for projectile motion are:
R = \frac{u^2 \sin(2\theta)}{g} and h = \frac{u^2 \sin^2(\theta)}{2g}.
Step 3: Given R = 2h, we can substitute the expressions for R and h in terms of u and \theta:
\frac{u^2 \sin(2\theta)}{g} = 2 \times \frac{u^2 \sin^2(\theta)}{2g}.
Step 4: Simplifying this gives: \sin(2\theta) = \sin^2(\theta).
Step 5: Using the identity \sin(2\theta) = 2\sin(\theta)\cos(\theta), we have 2\sin(\theta)\cos(\theta) = \sin^2(\theta).
Step 6: This simplifies to 2\cos(\theta) = \sin(\theta), or tan(\theta) = 2.
Step 7: Substituting back to find R in terms of h gives R = 4h, since R = 2h is 2 times the maximum height.
Therefore, the range of projection is 4h.