= 3. Four point masses m = m, m2 = 2m, m3 5m and m4 =...

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= 3. Four point masses m = m, m2 = 2m, m3 5m and m4 = m (here m is an arbitrary unit of mass) are located in the x-y plane with (x, y) coordinates (0, d), (2d, -d), (-d, d), and (2d, -5d), respectively. Here d is an arbitrary unit of length. a) Find an expression for the center of mass FCM in terms of d. Express this in terms of the distance from the origin and an angle with the x-axis. b) If the center of mass is a distance of 30 meters from the origin, what is d? c) Suppose m starts at the position given above but travels in the +y direction at a constant speed vo. Find an expression for the center of mass and the velocity of the center of mass as a function of time. What is the impulse on the system? You may leave your answers in terms of components. d) Now suppose m starts at rest at the same initial position as before but this time m is subjected to a constant force F=Fj. Find an expression for the center of mass and the velocity of the center of mass as a function of time. What is the impulse on the system and the momentum of the system as a function of time? You may leave your answers in terms of components. = 3. Four point masses m = m, m2 = 2m, m3 5m and m4 = m (here m is an arbitrary unit of mass) are located in the x-y plane with (x, y) coordinates (0, d), (2d, -d), (-d, d), and (2d, -5d), respectively. Here d is an arbitrary unit of length. a) Find an expression for the center of mass FCM in terms of d. Express this in terms of the distance from the origin and an angle with the x-axis. b) If the center of mass is a distance of 30 meters from the origin, what is d? c) Suppose m starts at the position given above but travels in the +y direction at a constant speed vo. Find an expression for the center of mass and the velocity of the center of mass as a function of time. What is the impulse on the system? You may leave your answers in terms of components. d) Now suppose m starts at rest at the same initial position as before but this time m is subjected to a constant force F=Fj. Find an expression for the center of mass and the velocity of the center of mass as a function of time. What is the impulse on the system and the momentum of the system as a function of time? You may leave your answers in terms of components.