Question 6 1 pts A body is projected vertically upwards with speed u in a medium that exerts a drag force -mKv, where K is a positive constant and is the velocity of the body. Find the maximum height reached by the body. uk Ok-m(1+) -In (1+ K² O + ²/(1+) O + n(1 + "K) K² On(1+K) In ug On(1+) Question 7 1 pts A body is projected vertically upwards with speed u in a medium that exerts a drag force -mKv, where K is a positive constant and is the velocity of the body. What is the TERMINAL SPEED? gt K K O-K 0- 9 Question 8 1 pts A particle is subject to uniform gravity and the linear resistance force -mkv, where K is a positive constant and is the velocity of the body. Initially the particle is projected with speed u in a direction making an angle a with the horizontal. Which of the following is TRUE about the subsequent motion? When uK/g is small, the time of flight is (2u/g) sin(2a). When uK/g is small, the time of flight is 2u sin(a/g). It has a vertical asymptote at x = (u/K) cos a. When uK/g is small, the range is (u²/g) sin(2a). It has a vertical asymptote at x = u cos(a/K) O O
Question 9 1 pts Suppose that, in the absence of damping, a physical system can perform free oscillations with angular frequency . Then a driving force with angular frequency wa will induce a large response in the system when wa is always very much less than wa is always very much greater than wa is always close to wa is close to , provided that the damping is not too large wa greatly differs from 2, provided that the damping is not too large Question 10 1 pts A particle P of mass 3m is suspended from a fixed point O by a light inextensible string of length a. A second particle of mass m is in turn suspended from P by a second string of length a. The system moves in a vertical plane through O. Let and be the angles that the two strings make with the downward vertical, and n² = g/a. Which of the following pairs are the linearized equations of motion for small oscillations near the vertical? Ö + 4 + 4n²0 = 0 and Ô +ệtn0 =0 ) 40 + ¢ + 4n²0 = 0 and ở tiệtn0 =0 40 ++4n30 =0 and Ô + − no = 0 OÖ + -4n²0 = 0 and Ô ++n20 =0 40 + 4 + 4n²0 = 0 and Ô + − n0 =0
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