Final Exam Versioll I Math110 A jet is flying through a wind that is blowing due

Question

Final Exam Versioll I Math110 A jet is flying through a wind that is blowing due East with a speed of 48 miles/hr. The jet has a speed of 720 miles/hr relative to the air, and the pilot heads the jet in the direction N 30° E. (Round your answers to one decimal place.) Express the velocity of the wind as a vector in terms of the vectors i and j a. Express the velocity of the jet relative to the air as a vector in terms of the vectors i and j b. c. Find the true velocity of the jet as a vector d. Find the true speed of the jet. (Round your answer to the nearest integer.) e. Find the direction of the jet. (Round your answer to the nearest integer.) 15

Explanation / Answer

ans for (a) :In part a we have to express the velocity of wind as a vector in terms of vectors i and j

wind =48sin(300)i +48cos(300)j =(48*0.5)i +(48*1.732/2)j =24i +41.5j

ans for (b) : The velocity of jet relative to air as a vector form is

jet = 720sin(300)i +720cos(300)j = 360i +622.5j

ans for part (c) :true velocity of jet as a vector is

jet =velocity of wind +velocity of jet =(24i +41.5j) +(360i +622.5j) =384i +664j

ans for part (d) :true speed of jet = square root of( (384)2 +(664)2) =767.04 mile/hr

ans for part (e) direction of jet :angle =arctan(384/664) = 30.04 0 jet's direction is N 30.040 E

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