Question

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 crane stands on a level ground. It is represented by a tower AB, of height 11 m and a jib BROTher 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.What is the length BS ? (a) 8√ 3 m (b) 4√ 3 m (c) 4√ 2 m (d) 8√ 2 m​

Answer 1

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

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