A stalactite in a cave has drops of waterfalling from it to the cave floor below. The drops are equallyspaced in time and come in rapid succession, so that at any givenmoment there are many drops in midair. (a) Is the center of massof the midair drops higher than, lower than, or equal to the halfway distance between the tip of the stalactite and the cave floor?(b) Choose the best explanation from among the following:I. The drops bunch up as they near the floor of the cave.II. The drops are equally spaced as they fall, since they are released at equal times.III. Though equally spaced in time, the drops are closer togetherhigher up

A game of billiards is being played with ball that are spherical shells of mass M and radiusR. Where should the ball contact the sharp edge of the bumper in order for there to be noreaction force of the ball on the felt?

The vector position of a 3.45 g particle moving in the xy plane varies in time according to i, - (3i + 35)t + 2jr? where t is in seconds and is in centimeters. At the same time, the vector position of a 5.20 g particle varies as i,- 31 - zir? - 6jt. (a) Determine the vector position (in cm) of the center of mass of the system at t = 2.90 s. x cm cm (b) Determine the linear momentum (in g cm/s) of the system at t = 2.90 s. 9. cm/s (e) Determine the velocity (in cm/s) of the center of mass at t = 2.90 s. cm/s (4) Determine the acceleration (in cm/s) of the center of mass at t = 2.90 s. cm/s? (e) Determine the net force (in µN) exerted on the two-particle system at t = 2.90 s. UN net

A 10 kg mass sits at (2 m, 0), a 15 kg mass sits at (0, -6 m) and a 25 kg mass is at (-2 m, 4 m). What are the coordinates of the center of mass?

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?