Two projectiles of mass m, and m, are fired at the same speed but in opposite directions from two launch sites separated by a distance D. They both reach the same spot in their highest point and strike there. As a result of the impact they stick together and move as a single body afterward. Find the place they will land. (Enter the distance from the site that launches m,. Assume that the launch sites are at the same height on the level ground. Use any variable or symbol stated above as necessary.)

A rocket takes off against the force of gravity. Consider this a non-isolated system. Derive the rocket equation formula relating velocity to the mass of the rocket and time. Let the velocity of the rocket be v(t) and the relative speed of the ejected fuel relative to the moving rocket be u. Ignore air drag.

Determine the coordinates of the center of mass of the three-particle system below.  The masses are as follows, m1=3.0 kg, m2 = 4.0 kg and m3 = 8 kg.  (Use xcm= (x1m1+ x2m2+ ...xnmn)/(m1+m2+...mn) and a similar formula for y.)  Assume ys= 2 m and xs=2 m.

A rocket of mass 10^5 kg is launched fromthe surface of the Earth. This is a sketch of the rocket as it’s still in Earth’s atmo-sphere. The rocket is undergoing an accel-eration of 3 m/s^2 upward. There is a forceexerted on the rocket from the thrust of itsengines labeled here as FEngine (you can useFE for short). The rocket is still close to theEarth’s surface, so it is subject to Earth’s gravity, and it is also subject to a substan-tial air resistance force. a. Draw a complete free body diagram of the rocket with all forces acting on it, clearlyindicating which direction each forces act.  b. What is the weight of the rocket, and what is the net force on the rocket? c. If the force the engine is exerting is FE = 1.8×10^6 N, what is the magnitude of the forceof air resistance? d. What is the work done by the engine as the rocket rises 150 m?