Question

Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. (a) What is the frequency (in hertz) of Tarzan's swing? (b) How long is the vine he is using?

Answer 1

Answer:

(a) 0.208 Hz

(b) 5.725 m

Explanation:

Tarzan completes 30 swings in 2.4 minutes

t = 2.4 minutes = 2.4 x 60 seconds = 144 s

Time period is defined as the time taken to complete one swing.

T = 144 / 30 = 4.8 s

(a) Frequency is defined as the reciprocal of time period. It is defined as the number of swings completed in one second.

$f = \frac{1}{T}=\frac{1}{4.8}$

f = 0.208 Hz

(b) Let the length of vine is L

The formula for the time period is given by

$T = 2\pi \sqrt{\frac{L}{g}}$

$4.8 = 2\times 3.14\sqrt{\frac{L}{9.8}}$

L = 5.725 m