Posted by Maria on Monday, November 21, 2011 at 8:47pm.
At t=0, ship A is 12 miles due north of ship B. Ship A travels 12 miles/hour due south, while ship B travels 8 miles/hour due east.
a. Write a function for the distance between the two ships.
b. At what time are the two ships closest?
Calculuss--Optimization - Reiny, Monday, November 21, 2011 at 11:16pm
At a time of t after t=0 , the southward distance covered by A is 12t miles, and the distance covered by B is 8t
Let the distance between them be d
I see a right - angled triangle.
a) d^2 = (8t)^2 + (12-12t)^2
dd/dt = 2(8t)(8) + 2(12-12t)(-12)
= 0 for a min d
128t -288 + 288t = 0
416t = 288
t = 288/416 = 9/13 = .6923
they will be closest at 9/13 hours
= .6923 hrs
= 41.5 minutes
at t = .6923 , d = 6.65640
take a value of t slightly higher and lower than .3923
t = .69 , d = 6.65648 , a bit farther than at t = .6923
t = .70 , d = 6.657 , a bit farther than at t = .6923
My answer is correct
Calculuss--Optimization - Maria, Monday, November 21, 2011 at 11:58pm
Thank you so much!
I appreciate it!
Answer This Question
More Related Questions
- Optimization--PLEASE HELP!!! - At t=0, ship A is 12 miles due north of ship B. ...
- calculus - Optimization At 1:00 PM ship A is 30 miles due south of ship B and is...
- Calculus - Ship A is moving east at 20 miles per hour, while ship B is moving ...
- CALCULUS!!!!! - At 9am, ship B was 65 miles due east of another ship, A. Ship B ...
- calculus - At 9am, ship B was 65 miles due east of another ship, A. Ship B was ...
- Calculus - One ship is 20 miles due North of another ship, and is sailing South ...
- precalulus - a ship travels 60 miles due east, then adjusts its course northward...
- Calculus - At 4 PM ship A is 40 miles due South Ship B. Ship A is sailing due ...
- Calculus - one ship (A) is sailing due south at 16 miles per hour and a second ...
- geometry - Two ships leave a harbor at the same time, traveling on courses that ...