Question

a body is thrown horizontally with a velocity root 2gh from the top of a tower of height h. it strikes the level ground through the foot of the tower at a distance x from the tower. ehat is the value of x??

Answer 1

Horizontal and vertical velocities are orthogonal to each other and therefore can be treated separately. We ignore air resistance.

Vertical motion is free fall under gravity and is governed by kinematic expression 
h=ut+12gt2
Time t to reach ground is
h=0×t+12gt2
⇒t=√2hg ......(1)
Final velocity as stone hits ground can be found with the help of kinematic expression
v=u+at
⇒vvf=0+g×√(2gh)
⇒vvf=√2gh

Horizontal motion.
Distance R moved during this time in the horizontal direction 
R=√2gh×√2hg=2h

We see that modulus of final vertical velocity is equal to horizontal velocity. As such resultant velocity as stone hits ground will make an angle of 45∘ with the y-axis. 
Also vR=√(√2gh)2+(√2gh)2
⇒vR=2√gh

Answer 2

Horizontal motion.

Distance

moved during this time in the horizontal direction= velocity*time

R=√2gh * root 2h/g

=2h