Tower cranes are a common fixture at any major construction site.
They’re pretty hard to miss -- they often rise hundreds of feet into the
air, and can reach out just as far. The construction crew uses the
tower crane to lift steel, concrete, large tools like acetylene torches
and generators, and a wide variety of other building materials. A crane stands on a level
ground. It is represented by
a tower AB, of height 11 m
and a jib BR. The jib is of
length 20 m and can rotate
in a vertical plane about B.
A vertical cable,RS , carries
a load S . The diagram
shows current position of
the jib, cable and load.
Q1) What is the length BS ?
(a) 8√ 3 m
(b) 4√ 3 m
(c) 4√ 2 m
(d) 8√ 2 m
Q2) What is the angle that the jib, BR, makes with the horizontal ?
(a) 450C
(b) 300C
(c) 600C
(d) 750C
Q3) What is the measure of the angle BRS ?
(a) 600C
(b) 750C
(c) 300C
(d) 450C
Q4) Now the jib BR, has been rotated and the length RS is increased.
The load is now on the ground at a point 8 m from A. What is the
angle through which the jib has been rotated ?
(a) 150C
(b) 250C
(c) 300C
(d) 450C
Q5) What is the length by which RS has been increased?
(a) 8 √3 m
(b) 8( √3 + 1) m
(c) 8( √2 + 1) m
(d) 8( √3 + 2) m
Answers
Given : Crane stands on a level ground.
It is represented by a tower AB, of height 11 m
jib is of length 20 m and can rotate in a vertical plane about B
A vertical cable, RS , carries a load S
The diagram shows current position of the jib, cable and load
BR = 16 , RS = 8
To Find : length BS
(a) 8√ 3 m
(b) 4√ 3 m
(c) 4√ 2 m
(d) 8√ 2 m
Solution:
BR = 16
RS = 8
Applying Pythagorean theorem :
BS² =BR² - RS²
=> BS² = 16² - 8²
=> BS² = 8²( 2² - 1)
=> BS² = 8²(4 - 1)
=> BS² = 8²(3)
=> BS = 8√3
length BS = 8√3 m
(a) 8√ 3 m is correct option
angle that the jib, BR, makes with the horizontal
Sin θ = 8/16
=> Sin θ =1/2
=> θ = 30°
∠BRS = 90° - 30° = 60°
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