While on a visit to Minnesota (\"Land of 10, 000 Lakes\"), you sign up to take a

Question

While on a visit to Minnesota ("Land of 10, 000 Lakes"), you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple harmonic motion with amplitude 20 cm. The boat takes 3.5 s to make one complete up-and-down cycle. When the boat is at its highest point, its deck is at the same height as the stationary dock. As you watch the boat bob up and down, you (mass 60 kg) begin to feel a bit woozy, due in part to the previous night's dinner of lutefisk. As a result, you refuse to board the boat unless the level of the boat's deck is within 10 cm of the dock level. How much time do you have to board the boat comfortably during each cycle of up-and-down motion?

Explanation / Answer

given

amplitude is 20 cm

using amlitude definition

considering the wave is completely sinusoidal wave

so one wave of crest is equal to 180 degree of the rotatory motion and also 10 cm high ( 10 cm dock level given )

now boarding into the boat anytime at the crest completely within 10 cm

so 180 degrees is half of 360 degrees available and also half of the 3.5 sec

so 3.5 / 2 = 1.75 sec

so amplitude maximum - displacement

then 1/3 of every cycle is available is 3.5 / 3

= 1.1666666 sec

the time do you have to board the boat comfortably during each cycle

of up-and-down motion is = 1.1666666 sec

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