There is a common fact about projectile motion. Let me remind you with an example: Assume that you are aiming at a hanging banana on a tree. If there were no gravitational force, the bullet would follow a linear path at a time "t". But since it does exist such kind of force, a parabolic path will occur. Now suppose that the banana suddenly began to free fall at the exact moment when you fired the gun -again with aiming at the banana's initial position. You will hit the banana literally. That is, the elapsed time for the free-fall of the banana and the projectile motion of the bullet are the same and equal to the certain "t" as stated above. Now my question is, how can we proof that with motion in 2D formulas?

(Banana is y meters above the ground. The diagonal distance between the shooter and the banana is z meters, also the shooter is x meters to the left for banana horizontally and they collide each other when the banana has already traveled over h meters.)


closed as off-topic by ACuriousMind, Carl Witthoft, Kyle Kanos, JamalS, Jim Dec 1 '14 at 20:42

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  • $\begingroup$ Just how did you come to think it's not a 2-D problem in the first place? $\endgroup$ – Carl Witthoft Dec 1 '14 at 20:15
  • $\begingroup$ Start by drawing the diagram (parabolic path and all) and writing the relevant equations. $\endgroup$ – Kyle Kanos Dec 1 '14 at 20:16
  • $\begingroup$ Nope, I didn't mean that. It is a 2D problem. $\endgroup$ – Pınar Dec 1 '14 at 20:26
  • 2
    $\begingroup$ @CarlWitthoft: I think you've misread the problem. OP wants to show that the collision occurs using 2D kinematics, not prove that it's a 2D problem. $\endgroup$ – Kyle Kanos Dec 1 '14 at 20:34
  • $\begingroup$ want to go on the record saying the bullet won't hit the banana if the gun is at a different height than it initially $\endgroup$ – Jim Dec 1 '14 at 20:41

1) What is the initial position of the bannana?

2) invent an initial position for the shooter.

3) at time 0, what is the direction of the bullet's velocity?

4) Now, set up a system of equations for the bullet and the bannana's motion.

5) do they hit each other?

  • $\begingroup$ I cannot eliminate variables. Too much of them that I can not substitute one thing to another. $\endgroup$ – Pınar Dec 1 '14 at 20:35
  • $\begingroup$ @Pınar that's because you haven't defined an initial height of the banana and the gun $\endgroup$ – Jim Dec 1 '14 at 20:40
  • $\begingroup$ @Pınar -- you won't be able to solve for everything in terms of a number like this (unless you do something like arbitrarily set the height of the bannana), you'll just be able to answer the question about whether or not their paths intersect. $\endgroup$ – Jerry Schirmer Dec 1 '14 at 20:42

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