Elmo's World

One day, Elmo decides he wants to be fired from a cannon.

• The location of the cannon is at 0x,
• 100z the angle between the $x$ -axis and the trajectory of Elmo is 45 degrees,
• the starting velocity of Elmo is $\sqrt{512} \text{ m/s}$ , and
• Elmo is on the planet called Elmoworld with the same gravity as this planet. The entire elmoworld is on the $xz$ plane and the only ground on Elmoworld that does not have 0z is 0x.

Find the $x$ -coordinate (the only non zero coordinate) of destination to 3 decimal places.

Assume $g= 10 \text{ m/s}^2$ .