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From top of a tower a stone is thrown up and it reaches the ground in time t1. A second stone is thrown down with the same speed and it reaches the ground in t2. A third stone is released from rest and it reaches the ground in time t3 then t3= ?
Dear Abhijeeth,
its very easy quest. we just need to find the values in u,g,and v(final velocity,this is constant for the first two cases)
for first throw.
t1= 2u/g + v-u/g=v+u/g
for second throw.
t2=v-u/g
for third release.
t3=u/g
so t3=(t1-t2)/2g. (ANS)
Regards.
Case(1)
let the intial speed be ''u'' and height be ''h''.
h(-j)=u(j)*t1+0.5g(-j)*t12
Case(2)
h(-j)=u(-j)*t2+0.5g(-j)*t22
Case(3)
h(-j)=0.5g(-j)*t32
solve case 1 and case 2 for t1 and t2 (quadratic) .
Applying equations of motion:
V= u+at
Let u= u1
a = g = 9.8m/sec2
We divide t1 into two timings , one for projectile motion and second part a stone travels from original position to ground.
So, t1=t’+t”
t’ = 2u1/g
t” = t2 as after stones reaches back original position it has velocity u1.
t1=2u1/g+t2
S= u1*t2+0.5*g*t2*t2 …………………………………(1)
So S= 0.5*g*t3*t3…………………………………………(2)
Solution : t3=sqrt(t1*t2)
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