Projectile Motion on a Hemispherical Rock: Finding the Minimum Initial Speed

[TheTaoOfBill]

Homework Statement

A person standing on top of a hemispherical rock (a dome rock) of Radius R kicks a ball (initially at rest on top of the rock) to give it horizontal velocity Vx

A. What must be it's minimum initial speed if the ball is never to hit the rock after it's been kicked?

B. With this initial speed. ow far from the base of the rock does the ball hit the ground

Homework Equations

Xf = V₀ + V_xiT + 1/2A_xT
V_x = VCos(theta)
V_y = VSin(theta)

The Attempt at a Solution

That's the thing I don't even know where to begin. I don't understand what it wants me to find. It gives no variables whatsoever!

 

[kjohnson]

You need to model the dome as a function (i.e a circle with equation x^2 +y^2=r^2 would work). Next you need to derive the position function for the ball. If you set them equal to each other you could solve for the time when the ball hits the rock. Since you want them not to hit, find the minimum value of v0 for which that applies.