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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Transcribed Image Text:on
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
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.
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, where
r> 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 at
any 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 an
amount of this material to decay to one-half its original value. Show
that for any radioactive material that decays according to the equation
Q' = -rQ, the half-life 7 and the decay rate r satisfy the equation
rT = ln 2.
12. According to Newton's law of cooling (see Problem 19 of
Section 1.1), the temperature u(t) of an object satisfies the differential
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