9 pl on9. Consider the falling object of mass 10 kg in Example 2, butassume now that the drag force is proportional to the square of thevelocity.a. If the limiting velocity is 49 m/s (the same as in Example 2),show that the equation of motion can be written asdvdt=1245 (492 - 1²).Also see Problem 21 of Section 1.1.b. If v(0) = 0, find an expression for v(t) at any time.G c. Plot your solution from part b and the solution (26) fromExample 2 on the same axes.d. Based on your plots in part c, compare the effect of aquadratic drag force with that of a linear drag force.e. Find the distance x(t) that the object falls in time t.Nf. Find the time T it takes the object to fall 300 m.10. A radioactive material, such as the isotope thorium-234,disintegrates at a rate proportional to the amount currently present.If Q(t) is the amount present at time t, then dQ/dt = -rQ, wherer> 0 is the decay rate.a. If 100 mg of thorium-234 decays to 82.04 mg in 1 week,determine the decay rate r.b. Find an expression for the amount of thorium-234 present atany time t.c. Find the time required for the thorium-234 to decay to one-half its original amount.11. The half-life of a radioactive material is the time required for anamount of this material to decay to one-half its original value. Showthat for any radioactive material that decays according to the equationQ' = -rQ, the half-life 7 and the decay rate r satisfy the equationrT = ln 2.12. According to Newton's law of cooling (see Problem 19 ofSection 1.1), the temperature u(t) of an object satisfies the differentialbatthewhvoCofWarapo

Given: Mass = m = 10 kg Limiting velocity= vL = 49 m/s Gravitational acceleration = g = 9.8 m/s2…

9. Consider the falling object of mass 10 kg in Example 2, but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as dv dt 1 1 245 (49² - 1²). Also see Problem 21 of Section 1.1. b. If v(0) = 0, find an expression for v(t) at any time. G c. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part c, compare the effect of a quadratic drag force with that of a linear drag force. e. Find the distance x(t) that the object falls in time t. N f. Find the time T it takes the object to fall 300 m.

9. Consider the falling object of mass 10 kg in Example 2, but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as dv dt 1 1 245 (49² - 1²). Also see Problem 21 of Section 1.1. b. If v(0) = 0, find an expression for v(t) at any time. G c. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part c, compare the effect of a quadratic drag force with that of a linear drag force. e. Find the distance x(t) that the object falls in time t. N f. Find the time T it takes the object to fall 300 m.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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