A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The intensity of light at point R at ground level on the street is proportional to the angle 0, in radians, where 0= ZPRQ as shown in the diagram. 10 m 9 m a m It is given that x is the distance of R from the base of the wall of height 10 metres. (i) Find an exact expression for 0 in terms of x, a and n. de (ii) Show that dr 10 9. Find, in terms of a, the value of x when the 100+x? (a-x) +81 intensity of light at R is maximum. (iii) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5 ms. Given that a = 20, find the rate of change of 0 at the instant when R is at the midpoint of the street. Give your answer correct to 4 significant figures. 10 tan 9. or 0 = tan [() 0 3 п - tan -1 -1 -1 a – x + tan 10 -1 X (ii) x = 10a – 3/10(a² +1), а - х 9 (iii) –0.0001381]
A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The intensity of light at point R at ground level on the street is proportional to the angle 0, in radians, where 0= ZPRQ as shown in the diagram. 10 m 9 m a m It is given that x is the distance of R from the base of the wall of height 10 metres. (i) Find an exact expression for 0 in terms of x, a and n. de (ii) Show that dr 10 9. Find, in terms of a, the value of x when the 100+x? (a-x) +81 intensity of light at R is maximum. (iii) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5 ms. Given that a = 20, find the rate of change of 0 at the instant when R is at the midpoint of the street. Give your answer correct to 4 significant figures. 10 tan 9. or 0 = tan [() 0 3 п - tan -1 -1 -1 a – x + tan 10 -1 X (ii) x = 10a – 3/10(a² +1), а - х 9 (iii) –0.0001381]
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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![A straight street of fixed width a metres on the horizontal ground is bounded on its parallel
sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The
intensity of light at point R at ground level on the street is proportional to the angle 0, in
radians, where 0 = ZPRQ as shown in the diagram.
10 m
9 m
R
am
It is given that x is the distance of R from the base of the wall of height 10 metres.
(i)
Find an exact expression for 0 in terms of x, a and T .
de
Show that
10
9.
(ii)
dr 100+x2 (a-x) +81
Find, in terms of a, the value of x when the
intensity of light at R is maximum.
(111) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5
ms. Given that a =
20, find the rate of change of 0 at the instant when R is at the midpoint
of the street. Give your answer correct to 4 significant figures.
10
[(1) 0 =
-1
T – tan
-1
tan
9
or 0 = tan
-1 a– x
+ tan
10
10a – 3/10(a² +1),
(ii) х %3D
а - х
9.
(iii) –0.0001381]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F902f5c45-8106-4c05-84fa-6818a38e7876%2F9f96dfff-b126-4273-b846-782e45fa03d6%2Ffj3tv4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A straight street of fixed width a metres on the horizontal ground is bounded on its parallel
sides by two vertical walls, one of height 10 metres, and the other of height 9 metres. The
intensity of light at point R at ground level on the street is proportional to the angle 0, in
radians, where 0 = ZPRQ as shown in the diagram.
10 m
9 m
R
am
It is given that x is the distance of R from the base of the wall of height 10 metres.
(i)
Find an exact expression for 0 in terms of x, a and T .
de
Show that
10
9.
(ii)
dr 100+x2 (a-x) +81
Find, in terms of a, the value of x when the
intensity of light at R is maximum.
(111) The point R moves across the street towards the wall of height 10 metres at a speed of 0.5
ms. Given that a =
20, find the rate of change of 0 at the instant when R is at the midpoint
of the street. Give your answer correct to 4 significant figures.
10
[(1) 0 =
-1
T – tan
-1
tan
9
or 0 = tan
-1 a– x
+ tan
10
10a – 3/10(a² +1),
(ii) х %3D
а - х
9.
(iii) –0.0001381]
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