CBSE Class 11-science Answered

Please answer!!!!!!

Asked by kpbhake | 24 Nov, 2017, 06:50: PM

Expert Answer

As per the figure, if R is the range in inclined plane, then horizontal distance travelled is Rcosφ and vertical distance travelled is Rsinφ.

time taken t for travelling Rcosφ is

begin mathsize 12px style t space equals space fraction numerator R cos phi over denominator v cos theta end fraction end style

using the equation for t, we can write for vertical distance

begin mathsize 12px style R sin phi space equals space v sin theta space open parentheses fraction numerator R cos phi over denominator v cos theta end fraction close parentheses space minus space 1 half g open parentheses fraction numerator R cos phi over denominator v cos theta end fraction close parentheses squared end style

Cancelling out the common R throught all the terms and multiplying all the terms by

begin mathsize 12px style fraction numerator 2 v squared cos squared theta over denominator g end fraction end style

we get

begin mathsize 12px style fraction numerator 2 v squared over denominator g end fraction cos squared theta sin phi space equals space fraction numerator 2 v squared over denominator g end fraction sin theta cos theta cos phi space minus space R space cos squared phi end style

By rearranging the terms

begin mathsize 12px style R cos squared phi space equals space fraction numerator 2 v squared over denominator g end fraction cos theta space open curly brackets sin theta cos phi space minus space cos theta sin phi close curly brackets space equals space fraction numerator 2 v squared over denominator g end fraction cos theta space sin left parenthesis theta minus phi right parenthesis end style

Hence

begin mathsize 12px style R space equals space fraction numerator 2 v squared over denominator g end fraction cos theta space fraction numerator sin left parenthesis theta minus phi right parenthesis over denominator cos squared phi end fraction end style

Answered by | 27 Nov, 2017, 02:48: PM

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