When Legolas the archer fires an arrow from his bow, its position can be described through the equations:

where x ₀ is the initial x-position [m], y ₀ is the initial y-position [m], v ₀ is the initial velocity [m/s], 9 is the launch angle [degrees], g = 9.81 m/s ² and t is time [s]. 1. Create a function that determines the x and y position of an arrow given initial conditions and a time vector are provided as inputs. 2. Create a function that plots the position of an arrow in the x-y plane given initial conditions and a time vector are provided as inputs. The plot should have axis labels and a title. 3. Create a function that can determine range (landing distance) of an arrow, given initial conditions are provided as inputs. Assume the ground is at y = 0. 4. Create a function that determines the magnitude and direction (in degrees) of velocity of an arrow given initial conditions and a time vector are provided as inputs.

x = xo + vo cos (0)t y = Yo + vo sin (0)t 1/2gt