Question

a body is thrown vertically upward,such that the distance travelled in 6th and 7th second of its motion are equal.The velocity with which body was projected from ground is??

Answer 1

Let a body is thrown vertically upward with velocity u .
we know, distance travelled in nth second is given $S_{nth}=|u-\frac{g}{2}(2n-1)|$

so, distance travelled in 6th second,
$S_{6th}=|u-\frac{g}{2}(2\times6-1)|\\\\=|u-55|$

distance travelled in 7th second,
$S_{7th}=|u-\frac{g}{2}(2\times7-1)|\\\\=|u-65|$

now, A/c to question,
$S_{6th}=S_{7th}$

|u - 55| = |u - 65|

u - 55 = -u + 65

2u = 55 + 65 = 120

u = 60 m/s

hence , velocity with which body was projected from the ground is 60 m/s.