Question

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?

Answer #1

The rate of change of distance between the two ships is 1 miles per hour.

The negative sign implies that the distance between the two ships is decreasing, i.e, they are getting closer.

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.)

At noon, ship A is 40 nautical miles due west of ship B. Ship A
is sailing west at 25 knots and ship B is sailing north at 20
knots. How fast (in knots) is the distance between the ships
changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per
hour.)
Note: Draw yourself a diagram which shows where the ships are at
noon and where they are "some time" later on. You will need...

At noon, ship A is 10 nautical miles due west of ship B. Ship A
is sailing west at 25 knots and ship B is sailing north at 23
knots. How fast (in knots) is the distance between the ships
changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per
hour.)
What is the answer in knots? Please neat answers only!

Ship A is 50 miles directly south of ship B at time t = 0. Ship
A is sailing east at 10 miles per hour while ship B is sailing
south at 15 miles per hour.
a. Is the distance between the ships increasing or decreasing
when ship A has traveled 10 miles to the east?
b. What is the rate at which the distance between the two ships
is changing when ship A has traveled 30 miles east?

Ships A and B leave port together. For the next two hours, ship
A travels at 40.0 mph in a direction 25.0 ∘ west of north while the
ship B travels 70.0 ∘ east of north at 30.0 mph.
A) What is the distance between the two ships two hours after
they depart?
It's NOT 56.67 miles
B) What is the speed of ship A as seen by ship B?

Two ships are on a collision course. At noon, ship A is
positioned 88 nautical miles (NM) due north of the collision point
and Ship B is 15 NM due east of the collision point. Ship A is
moving south with a constant speed of 16 knots.Ship B traveling
west with a constant speed of 30 knots. Calculate the rate of
change of the distance D between the ships at noon. dD/dt=?

At noon, ship A is 20 miles west of ship B. Ship A is traveling
due east at an average speed of 4mph, at the same time ship B
travels south at an average speed of 5mph. How fast is the distance
between ship A and B changing at 2:00pm?

At noon, ship A is 120 km west of ship B. Ship A is sailing
east at 20 km/h and ship B is sailing north at 15 km/h. How fast is
the distance between the ships changing at 4:00 PM?
km/h

A cruise ship heads due west from a port 4 miles directly south
of San Francisco. If the ship is travelling at a constant rate of
21 mph, how fast is the distance between the ship and San Francisco
changing 1 hour after leaving port? Round your answer to the
nearest tenth.

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...

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