(a) Find the differential equation satisfied by v(t) O A. dv V + dt 40 O B. dv V dt 40 None of the given answers is correct. dv dt C. O D. OE. = -9.81 v dv 10 dt = 9.81 +10v=19.62 = 19.62 (b) The velocity of the shell is: O A. v(t)=-392.4+492.4 e t 40 OB. None of the given answers is correct. O C. t 40 $ v(t)=-392.4 +492.4 e OD. v(t)=√10000 + 392.4t
(a) Find the differential equation satisfied by v(t) O A. dv V + dt 40 O B. dv V dt 40 None of the given answers is correct. dv dt C. O D. OE. = -9.81 v dv 10 dt = 9.81 +10v=19.62 = 19.62 (b) The velocity of the shell is: O A. v(t)=-392.4+492.4 e t 40 OB. None of the given answers is correct. O C. t 40 $ v(t)=-392.4 +492.4 e OD. v(t)=√10000 + 392.4t
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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Transcribed Image Text:(a) Find the differential equation satisfied by v(t)
A. dv V
dt
40
00
B. dv V
dt 40
+
D. dv
dt
OC. None of the given answers is correct.
O E.
= -9.81
= 9.81
v dv
10 dt
+10v=19.62
= 19.62
(b) The velocity of the shell is:
A.
v(t) = -392.4+492.4 e
t
40
OB. None of the given answers is correct.
O C.
t
40
v(t) = 392.4 +492.4 e
OD. v(t)=√10000 + 392.4t
Transcribed Image Text:Suppose that the vertical position axis x is oriented upward
A shell of mass 2 kg is shot upward with an initial velocity of 100 m/sec. The magnitude of the force due to air resistance is
with x = 0 at ground level. Denote by x(t) and v(t) the position and velocity of the shell at time t (in seconds). The acceleration due to gravity has magnitude g=9.81 m/sec².
20
The following numerical values might be useful in the calculations:
In 1.96= 0.764, In 98.04 =4.58, In 392.4 = 5.97, In 492.4 = 6.20
(a) Find the differential equation satisfied by v(t)
O A. dv V
+
dt 40
= -9.81
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