Answer to Question #83799 in Mechanics | Relativity for Era

Question

Is there a formula for calculating the range of a projectile under the influence of air resistance?

Answer 1

Unfortunately, no. Without air resistance the range depends on the angle α, initial velocity v, and the acceleration of gravity g only:

L=(v^2 sin⁡2α)/g.

With the influence of air resistance not only force of gravity is applied, but also force of air resistance, and calculations will be affected by the new net force:

F=mg-bv,

where b – coefficient of air resistance for body with mass m. The coefficient depends on shape and size of the body and its speed, so the range of a projectile under air resistance cannot be calculated analytically, only numerically for a given body with given properties.