What's the condition for maximum height and range in a normal projectile?

Answer 1

In a normal projectile motion, the conditions for maximum height and range are as follows:

Maximum Height:
The maximum height is achieved when the vertical velocity component becomes zero (at the highest point of the trajectory). This occurs when the object reaches the top of its trajectory and starts falling back down. At this point, the object's vertical acceleration due to gravity brings the object to rest before it starts descending.

Range:
The range is the horizontal distance traveled by the projectile. The maximum range is achieved when the launch angle is 45 degrees, assuming the initial and final elevations are the same. When the launch angle is 45 degrees, the horizontal and vertical components of the initial velocity are equal, resulting in the maximum forward motion while the object falls due to gravity. However, if the initial and final heights are different, the maximum range may not occur at 45 degrees.