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Solve this

Asked by venkat 25th December 2017, 9:06 PM
Answered by Expert
Answer:
Let U be the projection velocity at bottom of tower. Time taken by the ball and projection velocity U are related by the following equation
begin mathsize 12px style 0 space equals space U minus g t subscript 1 over 2 space space space left parenthesis space V space equals space U minus g t comma space V space i s space z e r o space a t space m a x i m u m space h e i g h t right parenthesis
h e n c e space U space equals space g t subscript 1 over 2 space.............................. space left parenthesis 1 right parenthesis end style
Let V be the velocity when it reaches top of tower and h is tower height. we can write the following equation for V
begin mathsize 12px style V squared space equals space fraction numerator g squared t subscript 1 superscript 2 over denominator 4 end fraction minus space 2 cross times g cross times h space...................... left parenthesis 2 right parenthesis space space space
space left parenthesis space V squared space equals space U squared minus 2 g h space i s space u s e d space i n space t h e space e q u a t i o n space g i v e n space a b o v e space right parenthesis end style
 
if V is the initial speed for the observer at the top of the tower, the time taken by the ball to reach maximum height from top of the tower can be obtained from the following equation.
 
begin mathsize 12px style 0 space equals space V minus g t subscript 2 over 2 space.................. left parenthesis 3 right parenthesis
left parenthesis space e q u a t i o n space v space equals space u minus g t space i s space u s e d space i n space left parenthesis 3 right parenthesis comma space a t space m a x i m u m space h e i g h t space v space equals 0 space right parenthesis

h e n c e space V space equals space g t subscript 2 over 2 space........... left parenthesis 4 right parenthesis end style
 
By using the equations (2) and (4), one can get  begin mathsize 12px style h space equals space g over 8 open parentheses t subscript 1 superscript 2 space minus space t subscript 2 superscript 2 close parentheses end style
Answered by Expert 27th December 2017, 1:00 PM
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