You are here:
Calculus/Question
Advertisement
Question
Intelligence reports to the U.S. fleet admiral the an enemy task force is located 120 nautical miles 42(degrees) east of north and is streaming 39(degrees)30(minutes) east of south at 25 knots.(1knot = 1nautical mile per hour).A destroyer group capable of 40 knots is dispatched to intercept the enemy.In what direction should they stream and how long will it take to intercept the enemy task force?
Please answer it with detail and provide a diagram also...
I have attached an image of a diagram that illustrate the vectors. We need to find θ & to .
)
To do so , we use the Sine rule .
Sine rule : x/sin(θ)=y/sin(42+39.5°) . Therefore : 25to/sin(θ)=40to/sin(42+39.5°), thus :
sin(θ)=(25/40)sin(42+39.5°)=0.6181 --> θ=38.18° , so the direction will be 38.18°+42° east of
north .
To find to to we apply the sine rule on the other side of the triangle :
25to/sin(θ)=120/sin(φ) --> 25to/sin(θ)=120/sin(180°-38.18°-81.5°) --> to=0.181 hour .
Alon.
Related Articles
Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience
1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
©2012 About.com, a part of The New York Times Company. All rights reserved.