1 mdv dt 10 dv dt = mg-bv; v(0) = v = (10) (9.81)-50 v
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can someone please tell me what I have done wrong or what I am missing in my work? I keep getting the wrong answer on this question, and I've attempted this same problem over 23 times. I DO NOT understand what I am doing wrong. Please tell me where I am messing up.

Transcribed Image Text:17 m dv = mg-bv; v(0) = v
dt
•10dv = (10) (9.81)-50 v
dt
• dv = 9.81 - 5vdt
.
dv = dt
9,81-5v
dv
9.81-5v
S
f=
du = S dt
-s(u)
In 19.81-5₁ = + + c
=
Sat
-S
(9.81-5v) = Cet
75-22 = 15-18'6
x = 9.81
X = 9.81
S
7
-Sv=Cest - 9.81
-St
v = Ce
S
-e
dx = 9,81 (¹-1)
dt
S
Sdx = 9.81
-1)dt
flest
- 241 (-6²² - +)*
S
·st
-e
t)
S
^5-186=1
75
du = -sdv
dv = du
-S
S
ce = 0 م
-t + 9.81
25
↑
v
1
(025-
s
0=(-9,81
|C=9.81
-St
9.81 ; √(0)=0 √= 9.81 st - 9.81
S
- 9.81
S
~0=(07x = 2 +
S
= 9.81 (e²³² - 1)
S
+ (0) - - - > -) 15³6 = 0 <
S
0=9,81
S
0= -9.81
3¹ (-/-) +
+C
as
C = +9.81
as
+(
+(

Transcribed Image Text:An object of mass 10 kg is released from rest 3000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object
with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m/sec² and let x(t)
represent the distance the object has fallen in t seconds.
First write m = mg - bv, v(0) = v in terms of the given information.
dv
dt
10 = 98.1 - 50v; v(0) = 0
dv
dt
Determine the equation of motion of the object.
x(t) = 1.962t - 0.3924 (1 - e¯5t)
When will the object hit the ground?
The object will hit the ground after seconds.
(Round to two decimal places as needed.)
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