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if a ball dropped from point P crosses point Q in t seconds. The time taken by it to travel from Q to R,if PQ=QR
Asked by mrudhulaprakashmanda844 | 23 Jul, 2022, 22:26: PM
answered-by-expert Expert Answer
If the ball is dropped at P, then initial speed of ball at P is zero.
 
If the ball reaches Q in time t , then speed u at Q is given as, 
 
u = g t ................................(1)
 
If the distance between P and Q is S1 , then we have
 
S1 = (1/2) g t2  .................................(2)
 
If distance S2 between Q and R is same as distance between P and Q , then
 
S2 = (1/2) g t2  .................................(3)
 
Let τ be the time taken from Q to R. Then distance travelled beween Q and R is determined from following equation
 
" S2 = u τ + (1/2) g τ2  "
 
If we use eqn.(1) and eqn.(3) in above equation of motion, we get
 
S2 = (1/2) g t2 = ( g t ) τ + (1/2) g τ2
 
Above expression is simplified as the following quadratic equation
 
τ2 + 2 t τ - t2  = 0
 
From above quadratic equation, we get ,  τ = ( √2 - 1 ) t
Answered by Thiyagarajan K | 23 Jul, 2022, 23:26: PM
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