This question is from Calc 3 and is most likely for people who have had calc-based physics. I was desperate for the off chance someone could do something for me! A projectile is launched from an initial position of r = (0,0,30)m with an initial velocity vector of v = m/s. What is the angle between the projectile velocity and the +Z axis at impact?

Question

This question is from Calc 3 and is most likely for people who have had calc-based physics.  I was desperate for the off chance someone could do something for me!

A projectile is launched from an initial position of r = (0,0,30)m with an initial velocity vector of v = <4,4,50> m/s.

What is the angle between the projectile velocity and the +Z axis at impact?

jamesj · Answer

Well, the velocity at time t is v(t) = <4,4,50-gt> and the position is
r(t) = (4t, 4t, -gt^2/2 + 50t + 30)

Now I assume 'impact' is when z(t) = 0, the z component of the displacement r.  Solve then for t and put that back into the expression for v(t).

Finally, the find the angle between v(t) and the z-axis, use the dot product.

anonymous · Answer

since you are giving initial then you are giving position at r(0)

anonymous · Answer

i think i have found something that you first have to integrate your velocity

jamesj · Answer

It was by integrating velocity we arrive at the function r(t)

anonymous · Answer

@salem: Yes, that initial is the position at r(0), I just wasn't entirely sure if I should actually write that.

And James, thank you for putting me on the right track!

anonymous · Answer

you should put it in term of vectors actually

jamesj · Answer

same difference.