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Home / Doubts and Solutions/JEE/Physics

A stone projected at an angle of 60 degree from the ground level strikes at an angle of 30 degree on the roof of a building of height h=30m ,find the speed of projection of the stone.

Asked by m.nilu 4th July 2018, 3:33 PM
Answered by Expert
Answer:
 
The figure is drawn as per my understanding of this question.
When the stone hits the roof, let us resolve the velocity vector into horizontal and vertical components as shown in figure.
 
Horizontal velocity component does not vary, hence it is u×cos60 = u/2.
we have assumed u is the intial velocity of projection.
 
Vertical velocity component v is given by
 
begin mathsize 12px style v squared space equals space u squared sin squared 60 space minus space 2 cross times 10 cross times 30 space equals space 0.75 u squared minus 600 space...................... left parenthesis 1 right parenthesis end style

In eqn.(1), for the conveneience of calculation,  it is assumed  that acceleration due to gravity g = 10 m/s2 .
From the vecor diagram of resolved velocity components, we can write

begin mathsize 12px style fraction numerator v over denominator begin display style bevelled u over 2 end style end fraction space equals space fraction numerator 2 v over denominator u end fraction equals tan 30 space equals fraction numerator 1 over denominator square root of 3 end fraction space space o r space 12 space v squared space equals space u squared space............. left parenthesis 2 right parenthesis end style

using (1) and (2), we can write begin mathsize 12px style 8 cross times u squared space equals space 7200 space o r space u space equals space 30 space m divided by s end style
Answered by Expert 5th July 2018, 11:48 AM
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