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## Homework Statement

I've been working out an example by myself from the book Adv. Engg. Mathematics, E.Kreszig, section 8.7 p441.

The path of a projectile traveling along a meridian of the earth uniformly may be given by

[tex]\vec{r(t)}=Rcos\gamma t\vec{b} + Rsin\gamma t\vec{k}[/tex] where i,j,k are unit vectors along x,y,z axes respectively.

The vector [tex]\vec{b}[/tex] is defined as [tex]\vec{b}=cos\omega t\vec{i} +sin\omega t\vec{j}[/tex]

Differentiating [tex]\vec{r(t)}[/tex] twice to get the expression for acceleration. This comes out to be

[tex]\vec{a(t)}=-R(\gamma ^2+\omega ^2)cos(\gamma t)\vec{b} -2R\gamma sin(\gamma t)\vec{b'} - R\gamma ^2cos(\gamma t)\vec{k}[/tex].

The first term is the centripital acceleration due to the earth and the path of the projectile, the second is the coriolis acceleration. What is the third term?