Kinematics

JEE Main level, numerical answer, medium

53 of 308

Question 53 of 308

Two spherical balls having equal masses with radius of 5cm5cm each are thrown upwards along the same vertical direction at an interval of 3s3s with the same initial velocity of 35ms−135m{s}^{-1}, then these balls collide at a height of _____mm,
(take g=10ms−2g=10m{s}^{-2})

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Answer: 50

S1=S2{S}_{1}={S}_{2}
35t+12(−g)t2=35(t−3)+12(−g)(t−3)235t+\dfrac{1}{2}(-g){t}^{2}=35(t-3)+\dfrac{1}{2}(-g)(t-3{)}^{2}
35t−12gt2=35t−35×3−12g(t2−6t+9)35t-\dfrac{1}{2}g{t}^{2}=35t-35\times 3-\dfrac{1}{2}g\left({t}^{2}-6t+9\right)
(35×3)+45=30t\left(35\times 3\right)+45=30t
t=15030=5t=\dfrac{150}{30}=5
heighth=35×5−12×10×52heighth=35\times 5-\dfrac{1}{2}\times 10\times {5}^{2}
h=175−125=50mh=175-125=50m

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