# soltn1 - Homework I Solutions 14(a In all casesone wants...

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Homework I Solutions 14 (a) In all cases one wants the speed of the plane relative to the ground. For the upwind and downwind legs, where o' in the figure is gven by (c2 - a2)V2 . L L z L ( 1 ' ) t",1= r_o+ ur=;lt_WI For the crosswind case, the plane's speed along t is o' =(r' -o')Ut . 2 L 2 L l - ,lc2 -uz , ,!t-1"1r72 o o crosswind t"=ffi(;,-n*r)=on",n 7-7 (b) At=t"+a-t,. =0.0085h=0.009h or 0.510 rnin =0-5 min This is a case of dilation. T = / T' in this pmblem with the prop€r time T'= 4 , =1,-(v\'f-" r^ -v-=1,-(!n\"l" . | \ c i I - " - c l - \ r / l I rr n1z)Uz r /1\1112 in thiscase r=2To,r=|'1-l+rl t =lt-lill therefore u=o.Wc. t L h J J t \ 4 i J The problem is solved by using time dilation. This is also a case of o << c so the binomial expansion is used u = yu' =l t + !]*', * - *' = S, " =f 4JU: * )]u" - L z c z ) - ' - - % 2 ' - | N ' ) ' WdayXs6n s/h) = o646st, N=N'-r=t16399s; , =fIE +m::!9!291! =t.44x 106 ny's.

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