Please answer!!!!!!

Asked by kpbhake | 24th 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  | 27th Nov, 2017, 02:48: PM