The three-dimensional motion of a particle is defined by the position vector: ~r = (Rt cosω n t) ~i + ct~j + (Rt sinω n t) ~k. Determine the magnitudes of the velocity and acceleration of the particle. show that the space curve described by the particle is a conic helix.

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.2-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kpa (gage) in the tank. if the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top in liters per second.

Aquick transition of the operating speed of a shaft from its critical speed will whirl amplitude. (a) increase (b) limit (c) not affect (d) zero