Question

a body is resting on top of a hemispherical mound of ice of radius r if ice is frictionless then what minimum horizontal velocity must must be imparted to the body so that it leaves the mould without sliding over it

Answer 1

Range = speed $\times$ time

h $=0.5gt^2$

So,

$$r=\frac{1}{2}gt^2\\or\\t=\sqrt\frac{2r}{g}$$

Range = $u\times t=u\times \sqrt\frac{2r}{g}$ $\ge r$

$$u\ge \sqrt\frac{gr}{2}$$