The tides at Cape Capstan New Brunswick change the depth of

The tides at Cape Capstan. New Brunswick, change the depth of the water in the harbor. On one day in October, the tides have a high point of approx. 10 m at 2 p.m. and a low point of approx. 1.2 m at 8:15 p.m. A particular sailboat has a draft of 2 m (this means that it can only move in water that is at least 2 m deep). The captain of the sailboat plans to exit the harbor at 6:30 p.m. Can the captain exit the harbor safely in the sailboat at 6:30 p.m.?

Solution

2)

height of tide function is of form y=Acos(Bx) +D

A=(10-1.2)_/2

A=4.4

at 2pm,t=0

at 8:15pm, t=(8+(15_/60))-2=6.25

time period= 2_/B=2*(6.25-0)

2_/B=2*(6.25)

B=_/6.25

B=0.16

D=(10+1.2)_/2

D=5.6

height of tide function is of form y=4.4cos(0.16x) +5.6

at 6:30pm, t=(6+(30_/60))-2 =4.5

height of tide at 6:30pm i.e, t=4.5 is y=4.4cos(0.16*4.5) +5.6

y=2.795m

2.795m >2m

so captain can exit harbour safely in the sailboat at 6:30 pm