Derive the differential equation(s) describing the given physical situation. Determine...

Derive the differential equation(s) describing the given physical situation.

Determine the equations of motion if the projectile in Problem 12 encounters a retarding force k (of magnitude k) acting tangent to the path but opposite to the motion. See Figure 1.21. [Hint: k is a multiple of the velocity, say cv.]

Problem 12:

A projectile shot from a gun has weight w = mg and velocity v tangent to its path of motion. Ignoring air resistance and all other forces except its weight, find the system of differential equations that describes the motion. See Figure 1.20. [Hint: Use Newton's second law in the x and y direction.]