(adsbygoogle = window.adsbygoogle || []).push({});

Hi Everybody,

I'm currently involved in a project in which I have to display the trajectory of a flying ball in 3D and predict its landing spot. My partners will track the ball as it is launched and give me a set of the ball's 3-D coordinates. The display path is easy but I have a few questions about the predicting path:

Normally, the object's landing spot in 2-D will be calculated by the following formula: (v^2*sin(2theta))/g

where v is the initial velocity, theta is the launching angle and g is gravity

Now, I never been exposed to projectile motion in 3-D and I have a few questions:

How do I extract the launching angle from a set of 3-D coordinates?

And I am thinking about using the 2-D equation above to calculate where the ball will land (in 2-D) and then somehow obtain the third dimension in the end...Is this a right approach ?

There was an answer from Arildno, Thanks Arildno:

"And I am thinking about using the 2-D equation above to calculate where the ball will land (in 2-D) and then somehow obtain the third dimension in the end...Is this a right approach ?"

This is a very good approach, because the the trajectory will lie in a plane whose vector normal is proportional to the cross product of the initial velocity vector and the constant acceleration vector

Hence, the trajectory curve is in essence a 2-D curve (its torsion zero).

As for expressing the launching angle, the closest analogy to the 2-D case is the polar (azimuthal??) angle in spherical coordinates.

But:

What does he means by:

"because the trajectory will lie in a plane whose vector normal is proportional to the cross product of the initial velocity vector and the constant acceleration vector"

I don't think I understand what he is saying? Can anyone help ???

Thanks a lot,

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Projectile motion again

**Physics Forums | Science Articles, Homework Help, Discussion**