The coordinates of a particle moving in a plane are given by 4 cos 6t and y = 6 sin 6t (a) find the equation of the path of the particle

concsider the two vectors A=3i-2j and B=-i-4j. calculate (a) A+B (b)A-B (c) |A+B| (d)| A-B| and(e)the directions of A+B and A-B

0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain