- #1

Moe777

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## Homework Statement

This is a quiz question that was given in my AP physics C class. "A rock is launched upward with a speed V

_{0}. With what velocity must a second rock be launched from the same initial position at time T later so that it hits the first rock when it has a velocity of -V

_{0}/2."

## Homework Equations

The only formulas we needed for this question were the basic velocity, displacement, and acceleration formulas (as functions of time) and their variations. (1D kinematics).

## The Attempt at a Solution

1) I drew a diagram on an axis with a vertical line (y axis) and the origin being zero (the initial position of the balls).

2) I listed all of the knowns and unknowns given from the question. We know that:

- Rock
_{1}(first rock) has an initial velocity of V_{0}. - Time= T
- Acceleration= -g= -9.81 m/s
^{2} - When the second rock hits the first rock, the velocity of the first rock will be -V
_{0}/2.

_{2}(second rock), which allows the given condition ( When the second rock hits the first rock, the velocity of the first rock will be -V

_{0}/2.) to happen. Basically, we don't know the initial velocity of rock

_{2}.

I then assumed the conditions for the collision:

When the rocks collide, they will be the same distance from the ground, so d

_{1}=d

_{2}

and I also assumed the time of travel for both rocks at the collision, which I put as T=T, which is where I'm sure that I made a mistake.

Since this is from a collected quiz, I don't remember exactly what I did. However, I remember doing something similar to this:

(-V

_{0rock1}/2)T- (1/2)gT

^{2}=( V

_{0rock2})T- (1/2)gT

^{2}

I forgot the process, but my solution was something like V

_{0}/2T, which is incorrect because the units come out to be m/s

^{2}. I feel that I did something completely off track, and I really need help as to how I should approach these problems and how to think more effectively. I felt as though this question should have been easier for me, which kind of discouraged me after that quiz was collected. This isn't the first time we get a question like this, and help for the question and questions like these would be much appreciated. Thank you in advance.

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