While on a visit to Minnesota (\"Land of 10,000 Lakes\"), you sign up to take an
ID: 2296308 • Letter: W
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 of 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 10cm of the dock level.
How much time do you have to board the boat comfortably during each cycle of up-and-down motion?
t = ?? s
I have no idea where to even start with this problem. Please show step by step so I can try to understand.
THANK YOU!!
Explanation / Answer
Amplitude is defined as the distance of a particle from rest position. Since amplitude is 20 cm, then, using above definition, Assuming the wave is purely sinusoidal, 1 wave crest equals180 degrees of rotary motion and is 10 cm high; ( and the trough is the other 180 degrees). You can therefore board the boat anytime during the crest and you are always withing 10cm of the dock. So you have 1/2 of 360 degrees available and half of 3.5 sec. That is 1.75 sec.
If by Amplitude you meant the maximum + And - displacement, then you have 1/3 of every cycle available, ie 1.17 sec.
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