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?
72 cl​

Answer 1

Solution :-

From image in Right ∆ ABC,

→ cos60° = (Base / Hypotenuse)

→ (1/2) = (r - 180) / r

→ 2r - 360 = r

→ 2r - r = 360

→ r = 360 .

Now,

→ Length of arc = 2πr * (@/2π) = @ * r ------- Eqn.(1)

Given that,

→ @ = 60° = (π/3) { As value of @ is in radian}.

Putting both values in Eqn .(1) we get,

→ Length of arc = (π/3) * 360

→ Length of arc = (22 * 360) / (7 * 3)

→ Length of arc = (22 * 120) / 7

→ Length 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.