a long fishing rod is kept upright .A boat engine causes the rod to vibrate.Mary speculates that the end of the rod moves to and fro 20 times in 1 minute.The amplitude of the vibrtion is 0.15m.Calculate the speed of the vibration at the end of the fishing rod
frequency f = 20 /60 = 1/3 Hz
x = .15 sin (2 pi (1/3) t)
v = .15(2 pi/3) cos (2 pi t/3)
= .1 pi cos (2 pi t/3)
or .1 pi maximum
To calculate the speed of the vibration at the end of the fishing rod, you can use the formula for the velocity of a wave. The speed of a wave (v) can be calculated by multiplying the frequency (f) of the wave by the wavelength (λ).
First, let's find the frequency of the vibration. Mary speculates that the end of the rod moves to and fro 20 times in 1 minute. The frequency (f) is the number of oscillations per second, so we need to convert 1 minute into seconds. Since there are 60 seconds in a minute, the frequency is 20 oscillations per 60 seconds, or 1/3 oscillations per second.
Next, we need to find the wavelength (λ) of the vibration. The wavelength is the distance between two corresponding points on the wave, which, in this case, is the distance traveled by the end of the rod in one complete to-and-fro motion. The amplitude (A) of the vibration is given as 0.15m.
Since the motion is to and fro, the distance traveled in one complete motion is double the amplitude. Thus, the wavelength (λ) is 2 times the amplitude.
Now, we can calculate the wavelength: λ = 2 * 0.15m = 0.30m.
Finally, we can calculate the speed (v) of the vibration using the formula v = f * λ:
v = (1/3 oscillations per second) * (0.30m) ≈ 0.10 m/s.
Therefore, the speed of the vibration at the end of the fishing rod is approximately 0.10 m/s.