Question

A swing base is 72 cm above the ground as shown in figure. When it travels through an angle of 60 ∘ from its mean position, swing base comes at 252 cm above the ground. What is the length of the arc travelled by the swing in meters?

Answer 1

Answer:

1.2π

Step-by-step explanation:

Here, difference between initial and final height =

252cm - 72cm = 180cm

                        = 1.8m

Now, as the swing is raised by 60⁰, Therefore, the radii of swing make an equilateral triangle with the line joining the given heights.

⇒ Line joining the heights makes an angle of 30⁰ with the straight line joining heights.

Let the radius be r;

then, sin 30⁰ = 1.8/r

       ⇒ 1/2 = 1.8/r

       ⇒ r = 3.6m

Now, length of arc = θ / 360 *2πr

                               =60/360*2π(3.6)

                                = 1.2π m

Answer 2

Given : A swing base is 72 cm above the ground as shown in figure. When it travels through an angle of 60∘ from its mean position, swing base comes at 252 cm above the ground.

To Find : length of the arc travelled by the swing in meters

Solution:

Let say Radius of Swing = R

Vertical  Distance of center   initially from ground = R + 72 cm

Vertical  Distance of center  after travelling 60° from swing base  

RCos60° = R/2

Vertical  Distance of center from ground  = 252 + R/2

R + 72  = 252 + R/2

=> R/2  = 180

=> R = 360  

Distance travelled in arc = (60/360)2πR

= (60/360)2π360

= 120π

= 377 cm

100 cm = 1m

= 3.77 m

length of the arc travelled by the swing in meters = 3.77

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