The position of the tin can over time is modelled by the functions ????(????) and ????(????), and the speed of the tin can over time is modelled by the functions ????????(????) and ????????(????), where x is the horizontal direction and y is the vertical direction, as shown in Figure 1. The drag forces ????????(????) and ????????(????) slow the projectile down in x and y direction, respectively. For low speeds, this force can be approximated as growing linearly with the relative speed of the projectile with respect to the breeze. Assuming a sea breeze with constant (negative) wind speed ????wx, the drag forces are: ????????(????)=????d(????????(????)????w????) and ????????(????)=????d????????(????)???? where ????d is the drag coefficient and ???? is the acceleration due to gravity. Our approximation uses Euler's integration method, which assumes that from the launch at time t=0, the projectile's movement is simulated in many very small time steps where during each time step the projectile moves a very small distance and its speed is diminished by a very small amount as well. During one time interval ????, the tin's position changes as: ????(????+????)=????(????)+????????(????)????

:????(????+????)=????(????)+????????(????)????

Initially we have ????(0)=????(0)=0, ????????(0)= ???? cos ????, and ????????(0)= ???? sin ???? where ???? is the launch speed and ???? the launch angle.

solving equation used to solve this equation