Physics: Can you help me, please?

[Reese Noreene]

1. What is the mathematical equation for a parabola shaped like a projectile's trajectory? How is the equation for a parabola similar to the equations for projectile motion?

2. You want to throw a banana up to a monkey sitting in a tree. The banana is directed straight toward the monkey as you release it. While throwing it you make a sound that scares the monkey. He jumps down from the tree at the instant you let go of the banana. Will the monkey catch it as he falls through the air?

3) A toy bird can easily be balanced on a fingertip, and it sways from side-to-side without falling if it is tapped. How do you think the bird balances this way?

***Any help is greatly appreciated! Thank you soo much!

[Phil H]

1.) Objects Trajectory: y=1/2at^2 + vt + y(initial)
Mathematical Parabola: y = ax^2+bx+c
The equations are similar because they are both quadratic equations.

2.) Yes, he will. Or at the very least it will hit him in the air. Gravity will have the same effect on the banana and the monkey. As the monkey falls, the banana will be arcing down at the same rate, so they will be in the same spot once the banana gets to the tree. Kind of hard to explain without a picture, but that's the general idea.

3.) Oddly, this has nothing to do with the concepts in the first two questions. In such a toy bird, the weight is situated so that the center of mass of the bird is below the point where the bird's beak is balancing on the stand. This makes the bird easy to balance and relatively stable on the stand.