There is a 1500 kg boat that's bobbing up and down in the waves in a lake, while its tied. The amplitude for its simple harmonic motion is 20 cm and the period is 3.5 s. When the boat is at its highest point, its deck is at the same height as the stationaty dock. A man (60 kg) is on the boat, and he wants to leave the boat when it is within 10 cm of the dock level. How much time does he have to board the boat comfortably during each cycle of up-and-down motion?
2007-09-23 06:09:58 · 1 answers · asked by Wolfgang M 1 in Science & Mathematics ➔ Physics
The masses are irrelevant. We have a ±20 cm motion and want to know how much of the cycle is > 10 cm.
At 10 cm height the angle from 0 is arcsin(10/20) = 30 deg
Then the region >10 cm extends 60 deg going from 30 deg to 90 deg, and another 60 deg from 90 to 30 deg on the other side, 120 deg in all. Thus the time > 10 cm = (120/360)*T = 1.17 s.
2007-09-23 07:30:25 · answer #1 · answered by kirchwey 7 · 0⤊ 0⤋