# Long-range artillery pieces are not set at the "maximum range" angle of 45° but at larger elevation angles, in the range of 55° to 65°. What is wrong with 45°?

Grade:upto college level

## 1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
In the absence of air resistance, the maximum range is achievable at an angle of elevation of 45° . However in the presence of the air resistance, the 45° angle of elevation does not ensure maximum range. This is due to the fact that the projectile no longer remains symmetrical when air resists the motion and the range of the projectile gets shorter.
The asymmetry in the projectile motion can be conceived from the figure below in which the angle at which the object hits the ground is -79° while the angle of elevation is 60°

It is important to note that the air resistance on smaller objects is proportional to their instantaneous velocity v. When an object moves toward the ground, the velocity of the object increases linearly and so does the air resistance. The increased air resistance reduces the range of the projectile and the object hits the ground at a larger angle.