# Differential Calculus

posted by .

At 9am ship B is 65 miles due east of another ship A. Ship B is then sailing due west at 10mi/h and A is sailing due south at 15 mi/hr if they continue in their respective course when will they be nearest to one another? and how near?

• Differential Calculus -

place ship B 65 miles east of ship A and mark them that way.
Let the time passed be t hrs
Draw a line BP , so that P is between A and B showing the distance traveled in those t hours.
Draw a line downwards AQ showing the distance traveled by ship A.
Join PQ to get the right-angled triangle APQ
AP = 65-10t
AQ = 15t
let D be the distance between P andQ

D^2 = (65-10t(^2 = (15t)^2
2D dD/dt = 2(65-10t)(-10) = 2(15t)(15)
for a minimum of D , dD/dt = 0
so 2(10)(65-10t) = 2(15t)(15)
divide by 10
2(65-10t) = 3(15t)
130 - 20t = 45t
65t = 130
t = 130/65 or 2 hrs

They will be closest at 9:00 + 2:00 or 11:00 am
and that distance is ....
D^2 = (65-20)^2 + 30^2
= 2925
D = √2925 = appr 54.1 miles

check my arithmetic

## Similar Questions

1. ### Calculus

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing at 3 PM?
2. ### 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?
3. ### Calculus

"At 9am ship A is 50 km east of ship B. Ship A is sailing north at 40km/h and ship B is sailing south at 30km/h. How fast is the distance between them changing at noon?
4. ### 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, find the rate at which the distance between the two ships is changing at 1:30 p.m.
5. ### 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?
6. ### calculus

At noon, ship A is 100 kilometers due east of ship B. Ship A is sailing west at 12 k/h and ship B is sailing S10degrees west at 10 k/h. At what time will the ships be nearest each other and what will this distance be?
7. ### calculus

At 9am, ship B was 65 miles due east of another ship, A. Ship B was then sailing due west at 10 miles per hour, and A was sailing due south at 15 miles per hour. If they continue their respective courses, when will they be nearest …
8. ### Calculus

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 24 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 6 PM?
9. ### CALCULUS!!!!!

At 9am, ship B was 65 miles due east of another ship, A. Ship B was then sailing due west at 10 miles per hour, and A was sailing due south at 15 miles per hour. If they continue their respective courses, when will they be nearest …
10. ### AP Calculus

Ship A is sailing due west at 8km/hr when it sees ship B northwest of its present position. If ship B is sailing due south at 3km/hr, then how close will they come on their courses?

More Similar Questions