The flight time of a shell shot at angle Φ and initial velocity V is T(f)= 2V/g sinΦ. Compute the average flight time for Φ in the interval [π/6,π/4]

QUESTION POSTED AT 28/05/2020 - 10:52 PM

Answered by admin AT 28/05/2020 - 10:52 PM

Flight time is
T= \frac{2V}{g} sin \phi

In the time interval [ \frac{ \pi }{6} , \frac{ \pi }{4} ], the average tme is
 T_{avg} = \frac{1}{ \frac{ \pi }{4}- \frac{ \pi }{6} } \int\limits^ \frac{ \pi }{6} _ \frac{ \pi }{4} {sin \phi } \, d \phi
=- \frac{24V}{g \pi } [cos \phi ] _{ \pi /6} ^{ \pi /4}
= \frac{24V}{ \pi g} (0.1589)
=1.214( \frac{V}{g} )

Answer:   T_{avg} =1.214( \frac{V}{g} )


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