Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv mmg -kv², k > 0 dt where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N. s/m after: a) 10 s b) 100 s c) 1000 s

At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing |- v³ E(v) = = V C vk s v-c. For Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)

High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s², and (2) the typical maximum speed attainable is about 8.8 m/s. You board an elevator on a skyscraper's ground floor and are transported 190 m above the ground level in three steps: acceleration of magnitude 1.2 m/s² from rest to 8.8 m/s, followed by constant upward velocity of 8.8 m/s. then deceleration of magnitude 1.2 m/s² from 8.8 m/s to rest. T Part A Determine the elapsed time for each of these 3 stages. Express your answers using two significant figures separated by commas. tace, tconstant, tdec = Submit Part B AFN,acc AFN,constant FN FN Submit Request Answer 2 [5] ΑΣΦ Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage. Express your answers using two significant figures separated by commas. 2 AFN,dec FN Request Answer Part C Complete…

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