Don’t Miss the Boat. 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 previ
ous 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?
ω : ω = 2π /T gives that x(t) = Acos(2π t/T)
The Attempt at a Solution
t = (T/2π )(1.047 rad) = (3.5 s/2π )(1.047 rad) = 0.583 s
2t = 2(0.583 s) =1.17 s.