Analyze the flight of a projectile moving under the influence of gravity (mg) and linear, i.e., laminar- flow drag (fD = bv, with b > 0 constant). Neglect \Phase I"; assume the projectile is launched from the origin at speed v1 and angle 1 above the horizontal. WARNING: Neither the results for the drag-free projectile nor those for the projectile with turbulent- flow drag can be applied directly to this problem; you must go back to basic principles. Part a) Write the equations of motion for the velocity components vx and vy of the projectile Part b) Determine the velocity components vx(t) and vy (t) of the projectile, as functions of time. Part c) Determine the position coordinates x(t) and y(t) of the projectile, as functions of time. I believe I have an idea for part b and c but cannot figure out how to put it in component form on part a.

To derive the equations of motion for the velocity components of the projectile, vx and vy, we can start by considering the forces acting on the projectile.

In this case, the projectile is subjected to two forces: gravity (mg) and linear drag (fD = bv). The force due to gravity acts vertically downward, while the force due to drag opposes the projectile's velocity and acts opposite to its direction of motion.

Using Newton's second law, we can write the equations of motion for the projectile in terms of its velocity components:

For the x-component:
m * ax = -bv_x,

For the y-component:
m * ay = -mg - bv_y.

Here, ax and ay represent the acceleration components in the x and y directions, respectively.

Next, we need to express these equations in terms of the velocity components vx and vy themselves, rather than their corresponding derivatives with respect to time.

To do this, we can use the fact that acceleration is the derivative of velocity with respect to time:

For the x-component:
m * d(v_x)/dt = -bv_x,

For the y-component:
m * d(v_y)/dt = -mg - bv_y.

Now, we have the equations of motion for the velocity components vx and vy in terms of their derivatives with respect to time.

For parts b and c, you can integrate these equations to obtain the velocity components vx(t) and vy(t) as functions of time (t), and then use these velocity functions to determine the position coordinates x(t) and y(t) of the projectile as functions of time.