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The data is recorded by a device and that the register are the:

- acceleration components along the (x, y, z),

- time (starting from 0, and change of each recording Delta t),

- orientation (azimuth, roll, pitch).

My goal is to be able to extrapolate a graph (elevation, time), the data is recorded by a device inside a passenger compartment, with the y-axis pointing upwards.

I read a lot about projectile motion, I think it's what I have to simulate substantially.

So for the calculation of the elevation, I would have thought to apply this formula:

vy = V_{iy} t + 1/2} a_y t^2

I thought to derive the speed through the Euler method, since dispose of acceleration and time data.

From this speed I should now extrapolate the vertical and horizontal speed, and if I understand correctly, the formula should be:

V_iy =V_i * sin (Φ)

the problem for me is to calculate precisely the angle Φ.

There is a way to calculate this angle?