Question

Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 13 miles per hour, and the other travels at a bearing of S 67° W at s miles per hour.

(a) Use the Law of Cosines to write an equation that relates s and the distance d between the two ships at noon.

(b) Find the speed s that the second ship must travel so that the ships are 42 miles apart at noon. (Round your answer to two decimal places.) mi/h

Answer #1

Two ships leave a harbor at the same time. One ship travels on a
bearing S10°W at 12 miles per hour. The other ship travels on a
bearing N75°E at 10 miles per hour. How far apart will the ships be
after 3 hours?

Ships A and B leave port together. For the next 4 hours, ship A
travels at 35 mph in a direction 40 degrees east of north while
ship B travels 70 degrees north of west at 25 mph. What is the
distance, in mi, between the two ships 4 hours after they
depart?

Ships A and B leave port together. For the next two hours, ship
A travels at 24 mph in a direction 30 degrees west of north while
ship B travels 28 degrees east of north at 29 mph .
a)What is the distance between the two ships two hours after
they depart?
b) What is the speed of ship A as seen by ship B?

Ship A is heading east toward a port at 20 mi/h and another ship
B is heading north from the port at 25 mi/h. How fast is the
distance S between two ships changing at the time when ship A is 30
miles away from the port and ship B is 40 miles from the port?
(Don’t forget to include units in your answer.)

One ship is approaching a port from the east, traveling west at
15 miles per hour, and is presently 3 miles east of the port. A
second ship has already left the port, traveling to the north at 10
miles per hour, and is presently 4 miles north of the port. At this
instant, what is the rate of change of the distance between two
ships? Are they getting closer or further apart?

A ship leaves port and travels due north at 15 knots for two
hours. Then it changes course to N 15° W. After another two hours
the ship stops. Draw a diagram that shows the path the ship has
sailed. What is the ships current distance from port?

Two ships leave a harbor entrance at the same time. The first
ship is traveling at a constant 16 miles per hour, while the second
is traveling at a constant 18 miles per hour. If the angle between
their courses is 146°, how far apart are they after 2 hours? (Round
your answer to the nearest whole number.)

A convertible and a minivan leave a highway junction at the same
time. The convertible travels west at 60 miles per hour and the
minivan travels north at 50 miles per hour. Assuming the two
vehicles do not deviate off course, how far apart are they after 4
hours?
Distance Apart =

Suppose that two boats leave a dock at different times. One
heads due north, the other due east. Find the rate at which the
distance between the boats is changing when the first boat is 67
miles from the dock traveling at a speed of 36 miles per hour and
the second boat is 89 miles from the dock traveling at a speed of
37 miles per hour.

5) Two high-speed ferries leave at the same time from a city to
go to the same island. The first ferry, the Cat, travels at
36 miles per hour. The second ferry, the Bird, travels at 23
miles per hour. In how many hours will the two ferries be 26 miles
apart?
The ferries will be 26 miles apart after ...hour(s).
6) Jane took 30 min to drive her boat upstream to water-ski at
her favorite spot. Coming back later...

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