- #1
teddy75
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Homework Statement
A person standing at the top of a hemispherical rock of radius R kicks a ball (initially at rest) to give it an initial horizontal velocity v0 What is the minimum initial speed for the ball not to hit the rock on its way down?
Homework Equations
[tex]x=v_0 t[/tex]
[tex]y=R-\frac{1}{2}g t^2[/tex]
The Attempt at a Solution
[tex]v_0^2t^2+R^2-2R\left(\frac{1}{2}gt^2\right)+\frac{1}{4}g^2t^4=R^2+2Rd+d^2[/tex]
[tex]v_0^2t^2+R^2-Rgt^2+\frac{1}{4}g^2t^4=R^2+2Rd+d^2[/tex]
[tex]v_0^2t^2-Rgt^2+\frac{1}{4}g^2t^4=2Rd+d^2[/tex]
Taking the derivative of d with respect to v0
[tex]2v_0t^2=2R\frac{dd}{dv_0}+2d\frac{dd}{dv_0}[/tex]
[tex]0=\frac{dd}{dv_0}}{d}[/tex]
[tex]0=\frac{v_0t^2-R}{d}[/tex]
[tex]v_0t^2=R[/tex]
Yeah... somehow I managed to screw that up so badly that not only did I get an equation with a t2 that I don't know what to do with, but I also got the units to not match up...