A spring$-$loaded cannon, with a spring constant k$,$ is mounted at the edge of a cliff which is h meters high. The cannon fires a projectile of mass m horizontally from the top of the cliff. The spring was compressed by a distance x to launch the projectile. When the projectile is launched, it enters a uniform circular motion due to a gravitational field before hitting the ground at a distance d from the base of the cliff.

$1.$ Calculate the initial velocity of the projectile as it leaves the spring$-$loaded cannon.

$2.$ Determine the time of flight before the projectile hits the ground.

$3.$ Calculate the centripetal acceleration of the projectile as it moves in circular motion due to gravity.

$4.$ Find the distance d from the base of the cliff where the projectile will land.

Include a clear labeled diagram of the situation $($with frames of refrence where applicable$)$