# Calculus

Two ships leave the same port at noon. Ship A sails north at 22 mph, and ship B sails east at 12 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

1. 👍
2. 👎
3. 👁
1. after t hours, the distance d is given in terms of the distances x east and y north,

d^2 = x^2 + y^2
2d dd/dt = 2x dx/dt + 2y dy/dt

at 1:00, x=12 and y=22, so
d^2 = 12^2 + 22^2
d = 25

so,

2*25 dd/dt = 2(12)(12) + 2(22)(22)
dd/dt = 25.12 mi/hr

1. 👍
2. 👎
2. QUESTION 3

A boat sails 30 miles to the east from a point P, then it changes direction and sails to the south. If this boat is sailing at a constant speed of 10 miles/hr, at what rate is its distance from the point P increasing

a) 2 hours after it leaves the point P
b) 7 hours after it leaves the point P

1. 👍
2. 👎

## Similar Questions

1. ### trig

Help! Ships A and B leave port at the same time and sail on straight paths making an angle of 60 degrees with each other. HOw far apart are the ships at the end of 1 hour if the speed of ship A is 25 km/h and that of ship B is 15

2. ### Math

A ship leaves port R sails to port S and then to port T. The bearing of S from R is 112. The Bearing of T from S is 033 The distance RT is 75 km and the distance RS is 56 km a) Draw a diagram showing the journey of the ship from R

3. ### Trig

Two ships leave the same port at 7.am. The first ship sails towards europe on a 54 degree course at a constant rate of 36 mi/h. The second ship,neither a tropical destination, sails on a 144 degree course at a constant speed of 42

4. ### pre-calc

a ship leaves port and sails for 2 hours north east and than 3 hours north west. If the speed remains constant, what course should the ship take home?

1. ### Trig

Two ships leave a harbor at the same time. One ship travels on a bearing S11 degrees W at 12 mph. The second ship travels on a bearing N75 degrees E at 9 mph. How far apart will the ships be after 3 hours?

2. ### Math

A ship leaves port R sails to port S and then to port T. The bearing of S from R is 112. The Bearing of T from S is 033 The distance RT is 75 km and the distance RS is 56 km a) Draw a diagram showing the journey of the ship from R

3. ### Math (Trig)

A ship leaves port at noon and has a bearing of S 25° W. The ship sails at 15 knots. How many nautical miles south and how many nautical miles west does the ship travel by 6:00 P.M.? (Round your answers to two decimal places.)

4. ### Math

Two ships leave the same port at the same time. One ship sails on a course of 110 degree at 32 mi/h. The other sails on a course of 230 degree at 40 mi/h. Find the distance between them after 2 hours. Express your answer to the

1. ### trigonometry

A ship leaves its home port and sails on a bearing N38°15'E at 24 mph.At the same instant,another ship leaves the same port on a bearing S51°45'E at 28 mph.Find the distance between the two ships after 8 hours.

2. ### Calculus

At noon of a certain day,ship A is 60 km due north of ship B. If A sails east at 12 km/hr and B sails north 9 km/hr,determine how rapidly the distance between them is changing 2 hrs later. Is it increasing or decreasing?

3. ### calc

At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM?

4. ### maths

a ships leaves port R, sails to S and then to port T. the bearing from R is 112, the bearing of T from S is 33 and the distance is 75km and the distance RS is 56. a) draw the diagram showing the journey of the ship from R to T.