Question

2. Galileo famously dropped two spheres of different weights (but of the same size) off of the Leaning Tower of Pisa in order to show that Aristotle's theory of gravity (that objects fall at rates proportional to their weights) was wrong. Suppose one sphere had mass m = 1 kg and the other had mass m = 5 kg, and that their velocities followed the equation: mv' = mg - kv with constant of proportionality k = 0.1 kg/s and acceleration g - -10 meters per second squared. (a) Solve for the velocity u(t) of each ball during the fall, assuming that each started with v(0) = 0. (b) How fast was each ball falling after 3 seconds? (c) For each ball, integrate v(t) to get d(t), the distance fallen, assuming d(0) = 0. (d) How far had each ball fallen after 3 seconds?

Answer 1

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o rit VB)=-100(1-2 Slio TV(3)=-25.9162 m=5 11=0.14 g=-10 Doo (le 1/60) V13) --500C-23160 V(3) = -29011 from @ ver) = m come tant) SUCH dta foretalhar e tintc, d10o =) mai cott 20)+9=0 G=-meg dinamo (t + 니 dch= machte e para mal, =0.1 =-10

Dorset d(3) = 25000 e so +2003 JOG+$Jaago = (IP +fensa 00og2 + (143971) ang- =(+3P ol=be lost ماده 3/10 01-20 t =(top olt ol+E) 201-JP 1+(94201+45 21-- -=Hip Ple) be