The correct option is A 1
Let the horizontal direction be along x− axis and vertical direction be along y− axis.
Given, the ball just hits the edge of the nth step.
So, total horizontal distance to be covered x=3×n=3n
and total vertical distance to be covered y=4×n=4n
Then, using the kinematic relation, s=ut+12at2
Along horizontal direction :
we can write that, x=uxt+12axt2
⇒3n=uxt [as ax=0]
Given, ux=36 m/s
⇒3n=36t ⇒t=3n36 ............(1)
Along vertical direction :
we can write that, y=uyt+12ayt2
From the data given in the question,
4n=12gt2 ...........(2)
From (1) and (2)
4n=12g(3n36)2
⇒n=g8×n2144=n2g1152
⇒n2g−1152n=0
⇒n=1152g or n=0 (trivial)
Comparing with n=1152αg, we get
α=1
Hence, option (a) is the correct answer.