A body of mass \( M \) thrown horizontally with velocity \( v \) from the top of the tower of height \( H \) touches the ground at a distance of \( 100 \, \text{m} \) from the foot of the tower. A body of mass \( 2M \) thrown at a velocity \(\displaystyle \frac{v}{2} \) from the top of the tower of height \( 4H \) will touch the ground at a distance of __________ \( \text{m} \).
