5. We want to find the effect of the Coriolis force on a trajectory. Consider a point on the earth's surface, P, where the angle between the vector connecting the center of the earth to P and the axis of rotation of the earth is o. We define a coordinate system at P with the z axis perpendicular to the ground, the r axis pointing south, and the y axis pointing east. A gun located at the origin of the coordinate system shoots a projectile with a velocity vo at an angle a in the +y direction. Taking account of the Coriolis force, the equations of motion of the projectile are mr = -2mw x v - mgz, or, in components, D = 2wvy cos o. y = 2w(vz sing + Ur cos o) Z = -g + 2wvy sino. (a) If we ignore the effects of the Coriolis force (this is equivalent to setting w equal to zero in the above equations) where will the projectile land? This is just a simple projectile problem in the y - z plane. (b) From part (a) you will get expressions for vr(t), Vy(t), and vz(t). Use these expressions and the above equations to find the x and y coordinates of the projectile when it hits the ground. This tells you the effect of the Coriolis force on the path of the projectile