# Path of a projectile traveling along a meridian of the earth

1. Feb 9, 2008

### chaoseverlasting

1. The problem statement, all variables and given/known data
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?

2. Feb 9, 2008

### pam

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

3. Feb 13, 2008

### chaoseverlasting

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