Question

Find the initial velocity of projection of a ball thrown vertically up if the distance moved by it in $3^{rd}$ second is twice the distance covered by it in $5^{th}$ second. (Take g $=$ 10 m s${}^{-2}$)

Answer 1

$S_{n}th=u+\frac{a}{2}(2n-1)$ [Distance traveled in nth second with constant acceleration]

$S_{3}rd=2S_{5}th$

$u-\frac{g}{2}(2\times 3-1)=2u-\frac{2g}{2}(2\times 5-1)$

$u-5\left(5\right)=2u-10\left(9\right)$

$90-25=2u-u=u$

$u=65m/s$