The vector position of a 3.65 g particle moving in the xy plane varies in time according to r, = (3î + 3j)t + 2jt? where t is in seconds and ris in centimeters. At the same time, the vector position of a 5.45 g particle varies as r, = 31 - 2it² – 6jt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.80 s. cm cm (b) Determine the linear momentum (in g· cm/s) of the system at t = 2.80 s. g. cm/s (c) Determine the velocity (in cm/s) of the center of mass at t = 2.80 s. Vcm = cm/s

Consider the following vectors: A   =  1.2i + 4.9j + 3.7k   B   =  -8.5i + 7.5j + 8.3k Part (a)  What is the x-component of the vector V = 3(A × 2B)?  Part (b)  What is the y-component of the vector V = 3(A × 2B)?    Part (c)  What is the z-component of the vector V = 3(A × 2B)?    Part (d)  What is the magnitude of the vector V?

A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)

Problem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.