A horizontal tree branch is directly above another horizontal tree branch. The e

Question

A horizontal tree branch is directly above another horizontal tree branch. The elevation of the higher branch is 9.78 m above the ground, and the elevation of the lower branch is 6.29 m above the ground. Some children decide to use the two branches to hold a tire swing. One end of the tire swing's rope is tied to the higher tree branch so that the bottom of the tire swing is 0.45 m above the ground. This swing is thus a restricted pendulum. Starting with the complete length of the rope at an initial angle of 14.2

Explanation / Answer

The time taken by the swing to go back:
T = (2*?*?(L1/g))/4 + (2*?*?(L2/g))/4

L1= pendulum length before hitting the lower brach = 9.78-0.45 = 9.33 m

L2=pendulum length after hitting the lower brach = 6.29 -0.45 = 5.84

=> T= 2.744 s

The time taken for back and forth = 2*T =2*2.744 = 5.487 s

Ans : 5.487s

NOTE: since the given angle is small (14.2), I have taken the time period of simple harmonic motion which is 2*?*?(l1/g). This is an approximated equation for small amplitudes. Hence it may be slightly different from the actual answer.

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