problem06_p102

University Physics with Modern Physics with Mastering Physics (11th Edition)

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6.102: In both cases, a given amount of fuel represents a given amount of work 0 W that the engine does in moving the plane forward against the resisting force. In terms of the range R and the (presumed) constant speed v , . 2 2 0 + = = v v R RF W β α In terms of the time of flight , , vt R T = so . 3 0 + = = v β v T vTF W α a) Rather than solve for R as a function of v , differentiate the first of these relations with respect to v , setting 0 0 = dv dW to obtain . 0 = + dv dF dv dR R F For the maximum range, , 0 = dv dR so . 0 = dv dF Performing the differentiation, , 0 2 2 3 = - = v β v dv dF α which is solved for
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Unformatted text preview: h. km 118 s m 9 . 32 m s N 30 . s m N 10 5 . 3 4 1 2 2 2 2 5 4 1 = = ⋅ ⋅ × = = β v b) Similarly, the maximum time is found by setting ; ) ( = Fv dv d performing the differentiation, , 3 2 2 =-v β v which is solved for h. km 90 s m 25 m s N 30 . ( 3 s m N 10 5 . 3 3 4 1 2 2 2 2 5 4 1 = = ⋅ ⋅ × = = β v...
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  • Calculus, Velocity, Nontotient, VT F.C.

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