Question

During a storm a ship is being tossed up and down by huge waves. The vertical motion of the ship is given by the equation: h = 21cos((2π/5)t) where h is height above sea level in feet at time t minutes.

1) Give the first 2 times that the ship is at sea level.
2) Give a general expression for the times at which the ship is at sea level.
3) When does the ship first fall to 17 feet below sea level?
4) Is the ship above sea level or below sea level at time 12 minutes?

Answer 1

(1) well, you want 2π/5 t = π/2 and 3π/2
so, that makes t = 5/4 for the first time.

Since the period is 2π/(2π/5) = 5, the second time is 5/2 later, at t=15/4

(2) from the period, this occurs at 5/4 + 5/2 k for integer k

(3) just solve for t in
21cos((2π/5)t) = -17

(4) same for t=2. h positive or negative?

See the graph at

http://www.wolframalpha.com/input/?i=21cos%28%282%CF%80%2F5%29t%29+for+0%3C%3Dt%3C%3D15