Projectile Motion with Linear DragThe main force affecting

Chapter 13, Problem 37E

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Problem        37E

Projectile Motion with Linear Drag

The main force affecting the motion of a projectile, other than gravity, is air resistance. This slowing down force is drag force, and it acts in a direction opposite to the velocity of the projectile (see accompanying figure). For projectiles moving through the air at relatively low speeds, however, the drag force is (very nearly) proportional to the speed (to the first power) and so is called linear.

Linear drag Derive the equations

by solving the following initial value problem for a vector r in the plane.

The drag coefficient k is a positive constant representing resistance due to air density, are the projectile’s initial speed and launch angle, and g is the acceleration of gravity.