Consider yourself as a physics expert. Imagine that there is...

Prompt

Consider yourself as a physics expert. Imagine that there is a dome and a projectile which needs to overcome the dome. Dome is hemisphere and diameter is on ground. Projectile needs to be shot from the ground and overcome the dome and land on the other side. The projectile needs to be above the dome at al times. Radius of Dome is 10m. Consider acceleration due to gravity as 9.8m/s^2. Determine the distance from the center of dome, angle of projectile and speed of projectile such that the speed of projectile is minimum and projectile overcomes the dome i.e. lands on the other side. The Projectile need not touch the dome at the top, overcome means it has to remain above the dome or glance it at one or two points. First provide the numerical answer, then provide the equation for V minimum, D (for vmin) and Angle (for vmin).