Sol. Method 1:

From trajectory equation

y = x tan θ –

y = x tan θ – (1 + tan 2 θ )

tan 2 θ – x tan θ + = 0

Putting x = d & y = h

tan 2 θ – d tan θ +

If projectile clears the pole then roots of above equation must be real

i.e. Discriminate > 0

d 2 – 4 > 0

1 – > 0

u 4 – (2gh) u 2 – g 2 d 2 > 0 ………….(i)

Let, u 4 – (2gh) u 2 – g 2 d 2 = 0

u 0 2 =

u 0 2 =

If u 2 > u 0 2 then expression (i) is greater than or equal to zero.

i.e. if u 2 > g

then projectile will clear the pole.

Sol. Method 2 :

sin α =

Maximum range of projectile on inclined plane is

R max =

If R max > ; then projectile will clear the pole

>

u 2 > g [h + ]