Rosencrantz, of mass m, has fallen out of the escape craft and is falling downward through Jupiter's atmosphere with vel

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Rosencrantz Of Mass M Has Fallen Out Of The Escape Craft And Is Falling Downward Through Jupiter S Atmosphere With Vel 1 (128.59 KiB) Viewed 11 times

Rosencrantz, of mass m, has fallen out of the escape craft and is falling downward through Jupiter's atmosphere with velocity v(t). He is subject to a uniform gravitational force F, = -mgy, as well as a quadratic drag force Fa = -buv = -bv²v. Poor guy. (a) Scene 1: Rosencrantz's Fall [3 pts] Write down the equation of motion for Rosencrantz's ill-fated trajectory as a differential equation for his velocity v(t). Show that his terminal velocity is vT = √mg/b, and rewrite the equation of motion in terms of g and UT, not in terms of m or b. Ⓒ2022 David Grabovsky. 4 This content is protected and may not be shared, uploaded, or distributed. (b) Scene 2: Analysis of the Fall [4 pts] 2 MORE DRAG AND ROCKETS [15 PTS] (b) Scene 2: Analysis of the Fall [4 pts] (i) Rosencrantz starts from rest at the origin of coordinates (located somewhere in the upper atmosphere of Jupiter) at t = 0. Show that his subsequent trajectory is gt y(t): = 9 In cosh (2.1)