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?
Answers
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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From image in Right A ABC,
+ >cos 60° = (Base / Hypotenuse)
>(1/2) = (r - 180) /r
- >2r - 360 =r
- >2r -r = 360
>r = 360.
Now,
» Length of arc = 2r * (@/2n) = @ * r
(1)
Given that,
- @ = 60° = (1/3) { As value of @ is in radian.}
Putting both values in Equation .(1) we get, Length of arc = (1/3) * 360
- Length of arc = (22 * 360) / (7 * 3)
Length of arc = (22 * 360) / (7 * 3)+ Length of arc = (22 * 120) / 7
Length of arc = (22 * 360) / (7 * 3)+ Length of arc = (22 * 120) / 7Length of arc = = (2640/7)
Length of arc = (22 * 360) / (7 * 3)+ Length of arc = (22 * 120) / 7Length of arc = = (2640/7)Length of arc = 377 cm.
Now,
100cm = 1 m.
+>1 cm = (1/100)m
+> 377cm = (1/100) * 377 = 3.77m.(Ans.)
Hence, Length of the arc travelled by the swing is 3.77m.
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