From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

Step 1: Time taken to reach the maximum height(t1)[Ref. Fig.]
At maximum height V=0
Since acceleration is constant, therefore applying equation of motion in y direction. Taking upward positive
V=u+at1[a=-g m/s2]
→0=u-gt1
→t1=u/g (1)
Step 2: Time taken to hit the ground(t2)
Applying the 2nd equation of motion
s=ut2+1/2at22[s=-H]
→-H=ut2-1/2gt22 (2)
Given that t2=nt1=nu/g (3)
Step 3: Solving above equations
Substitute the value of t2 from (3) in (2)
-H=u×nu/g -1/2g×n2u2/g2
→2gH=nu2(n-2)
Hence, Option A is correct.