Calculus

posted by .

At 1:00 p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16km/h and ship B is sailing south at 20km/h, find the rate at which the distance between the two ships is changing at 1:30 p.m.

• Calculus -

draw the triangle (lets W, S)

label the West leg W km, South leg Skm

Distance between ship x.

x= sqrt (W^2+S^2)
dx/dt= 1/2 *1/sqrt( ) * (2w *dw/dt + 2S ds/dt)

find dx/dt

Caculate S, W from 1/2 hr at given speeds.
you know dw/dt, ds/dt

• Calculus -

xa = -16 t
ya = 25

xb = 0
yb = -20 t

at 1/2 hour
xa = -8
ya = 25

xb = 0
yb = -10

z = distance between
z^2 = (xb-xa)^2 + (yb-ya)^2
z^2 = (16 t)^2 + (-20 t - 25)^2
2z dz/dt = 2(16t)(16) + 2(-20t-25)(-20)
z dz/dt = 256 t +400 t + 500
z dz/dt = 656 t + 500
now at 1/2 hour
z = sqrt(64 + 1225) = 35.9
so
35.9 dz/dt = 328+500
dz/dt = 23.1 km/hr

• Calculus -

THANKS FOR ALL THE HELP!

One question, how do you find xa,ya, xb, and yb?

• Calculus -

xa is the x position of the first ship
At time 0 it is at x = 0
then it proceeds in the west (negative x) direction at 16 km/hr
so the x position of A is (0 - 16 t) or just -16 t
Since it starts out 25 km north (positive y directio) and never goes north or sout, its Y position is always ya = 25
etc

• Calculus -

Oh i shoud've been more specific, what i meant to ask was how do you find xa, ya etc. at 1/2 hours?

• Calculus -

OH NEVER MIND! I GOT IT HAHAHA!

• Calculus -

Can you use that distance equation every problem or is it modified to fit this question?
Also, how did you find z at 1/2 hours? (z = sqrt(64 + 1225) = 35.9)?

Similar Questions

1. calculus

Optimization At 1:00 PM ship A is 30 miles due south of ship B and is sailing north at a rate of 15mph. If ship B is sailing due west at a rate of 10mph, at what time will the distance between the two ships be minimal?
2. calculus

At noon, ship A starts sailing due east at the rate of 20km/hr. Ath the time, ship B, which is located 100km east of ship A initially, starts sailing on a course 60 degrees north of west at the rate of 10km/hr. How fast is the distance …
3. calculus

At 1:00 p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16km/h and ship B is sailing south at 20km/h What is the first time after 3:00 p.m. that the hands of the clock are together?
4. Derivatives

Ship A is 70 km west of ship B and is sailing south at the rate of 25 km/hr.ship B is sailing north at the rate of 45 km/hr.how fast is the distance between the two ships changing 2 hours later?
5. Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between …
6. Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between …
7. Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between …
8. Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between …
9. Calculus 1

Related Rates I am having trouble finding the equation to use to fit this all together. At noon, ship A is 100km west of ship B. Ship A is sailing south at 35 km/s and ship B is sailing north at 25 km/s. How fast is the distance between …
10. Calc

At noon, ship A is 100km west of ship B. Ship A is sailing south at 30km/h and ship B is sailing north at 15km/h. How fast is the distance between the ships changing at 4:00pm?

More Similar Questions