Problem 7: Consider a particle of mass m = 1kg subject to the effects of gravity in the downward direction and a drag force in the direction opposite to the velocity of the particle and of magnitude |D| = cvP where c 1sa constant and v 1s the speed of the particle. a) Write the equations of motion of the particle in cartesian coordinates. Ans: m = ci(yF +52) andmy = cy(JFZ +52) mg b) Solve the equations of motion to get x(t) and y(t) by hand for the following cases. 1) c=0 Ans: This 1s a familiar case! ) p=1,c#0 Ans: y(t) = %(j}o + %) (1 - e\"Ft) %t +y,. x(t) = mx, c (1 e_%t) + X