8.A boat is traveling at 1.7m/s in the same direction as an ocean wave of wavele

Question

8.A boat is traveling at 1.7m/s in the same direction as an ocean wave of wavelength 30 m and speed 6.8 m/s.
If the boat is on the crest of a wave, how much time will elapse until the boat is next on a crest?
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5.A spring scale hung from the ceiling stretches by 5.4cm when a 2.0kg mass is hung from it. The 2.0kg mass is removed and replaced with a 2.2kg mass.
What is the stretch of the spring?

7.The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.22Hz , and the acceleration of the top of the building can reach 1.8% of the free-fall acceleration, enough to cause discomfort for occupants.

What is the total distance, side to side, that the top of the building moves during such an oscillation?

Explanation / Answer

vb = 1.7 m/s, V = 6.8 m/s

lambda = 30 m

The relative speed of the boat vr = - 1.7 + 6.8 = 5.1 m/s

d = lambda = 30 m

t = d / vr= 30 m / 5.1m/s

t = 5.88 sec

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5) F = k x

m1 g = k x1 , m2 g = k x2

m2 g / m1 g = k x2 / k x1

x2 = x1 [m2 / m1] = 5.4 [2.2  / 2.0]

= 5.94 cm

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7) The maximum acceleration is a = A * w2 = 0.018 * 9.81 = 0.177 m/s2

w = 2 pi * f = 2 pi * 0.22 Hz = 1.38 rad/s

A = 0.177 / 1.382 = 0.0929 m

Total side-to-side distance = 2A = 0.186 m = 18.6 cm

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