A stone is projected from top of a vertical pole of height 3 m with initial velocity 10 ms-1. The maximum range on the ground is 10x m. The value of x is _____.

Let stone is projected at an angle α with horizontal.∴  (ucos⁡α)t= Range =R and −3=(10sin⁡α)t−12×10×t2From Eqs. (i) and (ii), we getR2+5t2−32=100t2⇒R2+25t4+9−30t2=100t2⇒25t4−130t2+9+R2=0The discriminant of quadratic in t2 should be greater or equal to zero.∴    D≥0⇒    (−130)2−4×259+R2≥0⇒    16900≥1009+R2⇒    9+R2≤169⇒    9+R2≤169⇒    R2≤160∴    R≤160∴    Rmax=410m∴     x=4