A, B, and C must be in vector component form A jet is flying through a wind that

Question

A, B, and C must be in vector component form

A jet is flying through a wind that is blowing with a speed of 50 mi/h in the direction N 30 E (see the figure). The jet has a speed of 760 mi/h relative to the air, and the pilot heads the jet in the direction N 45° E 300 MUST BE IN VECTOR FORM (a) Express the velocity of the wind as a vector in component form. (b) Express the velocity of the jet relative to the air as a vector in component form (c) Find the true velocity of the jet as a vector. (Round your answer to two decimal places.) (d) Find the true speed of the jet. od your answer to the nearest integer) mi/h Find the direction of the jet. (Round your answer to the nearest integer)

Explanation / Answer

w=wind,g=ground,j=jet,v=velocity

(a)

velocity of the wind ,vwg = 50cos(90o-30o)i +50sin(90o-30o)j

=>vwg = 50cos(60o)i +50sin(60o)j

=>vwg = 25i +253j

(b)

velocity of the jet relative to the air ,vjw = 760cos(90o-45o)i +760sin(90o-45o)j

=>vjw = 760cos(45o)i +760sin(45o)j

=>vjw = 3802 i +3802 j

(c)

true velocity, vjg=vjw+vwg

=>vjg=(3802 i +3802 j)+(25i +253j)

=>vjg=(3802 +25) i +(3802 +253) j

=>vjg=562.40 i +580.70 j

(d)

true speed =[562.402+580.702]

true speed =808 mi/h

direction = N(90o-tan-1(580.70/562.40))E

direction = N44o E

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