Path of a projectile traveling along a meridian of the earth

[chaoseverlasting]

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

The vector $$\vec{b}$$ is defined as $$\vec{b}=cos\omega t\vec{i} +sin\omega t\vec{j}$$

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

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

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?

 

[pam]

It is the z component of the centripetal acceleration.
It should have sin\gamma t.

 

[chaoseverlasting]

Oh. ! thank you. That was incredibly stupid of me.