At a concert, a band is playing on a platform that extends P feet from a wall behind the band, and the platform is rising from ground level, as shown in the figure above. A light source is L feet from the wall, and the platform casts a lengthening shadow on the wall as the platform rises. At time t seconds, the platform is h feet above the ground, and the height of the shadow is s feet. The quantities are related by the equation (h+s) = s, where L and P are constants. Which of the following best expresses the rate of change of h with respect to time in terms of the rate of change of s with respect to time?
At a concert, a band is playing on a platform that extends P feet from a wall behind the band, and the platform is rising from ground level, as shown in the figure above. A light source is L feet from the wall, and the platform casts a lengthening shadow on the wall as the platform rises. At time t seconds, the platform is h feet above the ground, and the height of the shadow is s feet. The quantities are related by the equation (h+s) = s, where L and P are constants. Which of the following best expresses the rate of change of h with respect to time in terms of the rate of change of s with respect to time?
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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At a concert, a band is playing on a platform that extends P feet from a wall behind the band, and the
platform is rising from ground level, as shown in the figure above. A light source is L feet from the wall, and
the platform casts a lengthening shadow on the wall as the platform rises. At time t seconds, the platform
is h feet above the ground, and the height of the shadow is s feet. The quantities are related by the equation
(h+s) = 8, where L and Pare constants. Which of the following best expresses the rate of change
of h with respect to time in terms of the rate of change of s with respect to time?
dh
dt
s ft
dh = 1 d
h ft
=8 S
18-d
L ds
P dt
8
-P ft-
ds
dt.
L ft
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