Projectile Motion and its Parameters:
Projectile motion is the motion of an object thrown into the air, under the influence of gravity, with an initial velocity. The object follows a curved path known as a parabola.

Some key parameters of projectile motion are:
1. Initial velocity (u): The velocity with which the object is projected.
2. Angle of projection (θ): The angle at which the object is projected with respect to the horizontal axis.
3. Range (R): The horizontal distance covered by the object before it hits the ground.
4. Maximum height (H): The highest point reached by the object during its motion.

Derivation of the Range and Maximum Height:
To find the range (R) and maximum height (H) of a projectile, we need to analyze the motion in the horizontal and vertical directions separately.

1. Horizontal Motion:
In the absence of air resistance, the horizontal component of velocity remains constant throughout the motion. So, the time taken to reach the maximum height (T) is equal to the time taken to return to the same horizontal level.

2. Vertical Motion:
The vertical component of velocity changes due to the acceleration due to gravity (g). At the maximum height, the vertical component of velocity becomes zero. Using the kinematic equation, we can find the time taken to reach the maximum height.

3. Equating Time of Flight:
Since the time taken to reach the maximum height and return to the same horizontal level is equal, we can equate the time of flight in the horizontal and vertical directions.

4. Range and Maximum Height:
By substituting the value of time (T) in terms of initial velocity (u) and angle of projection (θ), we can derive the expressions for range (R) and maximum height (H).

Answer:
When the range and maximum height of a projectile are the same, it implies that the time of flight in the horizontal and vertical directions is equal. Therefore, the range (R) and maximum height (H) can be calculated using the following equations:

Range (R) = (u^2 * sin(2θ))/g

Maximum Height (H) = (u^2 * sin^2(θ))/(2g)

Explanation:
When the range and maximum height are equal, we can equate the above two equations and solve for the angle of projection (θ). Once we find the value of θ, we can substitute it back into either of the equations to calculate the common value of range and maximum height.

Note: The given problem does not provide any specific values for the initial velocity (u) or the angle of projection (θ). Therefore, the exact numerical value of the maximum height cannot be determined without these parameters. However, the relation between the range and maximum height has been explained above.