A boy travels 12km east wards to a point B and then 5km southwards to another point C. Calculate the difference between the magnitude of the displacement of the boy and the distance travelled by him.

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 11.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.80 m/s; (b) he is then lifted at the constant speed of 4.80 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 78.0 kg rescue by the force lifting him during each stage

During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. if the trebuchet launches the stones with a velocity of at an angle of 50.0°, (a) how long does it take the stone to hit the ground? (b) what is the maximum distance that the trebuchet can be from the castle wall to be in range? (c) how high will the stones go? show all your work.

Engines for propeller-driven aircraft are limited in their maximum rotational speed by the fact that the tip speed of the propeller must not approach the speed of sound in air (mach i). taking 6 ft as a typical diameter for a propeller of a light airplane and 1100 fils as the speed of sound, find the upper limit on the rpm (revolutions per minute) of the propeller shaft.