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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 23rd July 2022, 10:26 PM
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 Expert 23rd July 2022, 11:26 PM
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