After school you have been working on your slingshotmanship. Interested in the physics of the slingshot, you take data that compares the force of the extended slingshot versus the displacement from equilibrium. You think this graph is very similar to that of a spring so you decide to solve for the spring constant of the rubber band. If the slingshot is stretched back 30 centimeters and released about how much energy is put into a 50 gram Rock? What is the velocity of the rock upon release from the slingshot?

To solve this problem, we need to make some assumptions and use a basic formula from physics. Here's how you can approach it:

1. Assumptions:
- Assume that the slingshot behaves like a Hooke's Law spring. This means that the force exerted by the slingshot is directly proportional to the displacement from equilibrium.
- Assume that the motion of the slingshot is one-dimensional, neglecting any air resistance or other external factors.

2. Hooke's Law:
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from equilibrium. The formula is F = k * x, where:
- F is the force applied by the spring,
- k is the spring constant (a measure of stiffness), and
- x is the displacement from equilibrium.

3. Analyzing the problem:
- In this case, we can consider the displacement from equilibrium as the distance the slingshot is stretched back, which is given as 30 centimeters.
- We don't have the spring constant, but we can find it by analyzing the data that compares the force of the extended slingshot versus the displacement from equilibrium.

4. Finding the spring constant:
- Plot the data comparing the force of the extended slingshot versus the displacement from equilibrium on a graph.
- Fit a line to the data points. This line represents the relationship between force and displacement.
- The slope of this line will give you the spring constant (k). You can calculate it using the formula k = (force on the slingshot) / (displacement from equilibrium).

5. Calculating the energy:
- Once you have the spring constant (k), you can calculate the potential energy (PE) stored in the slingshot when it is stretched. The formula is PE = (1/2) * k * x^2, where:
- PE is the potential energy,
- k is the spring constant, and
- x is the displacement from equilibrium (30 centimeters).

6. Calculating the velocity:
- To find the velocity of the rock upon release, you can use the principle of conservation of mechanical energy.
- When the rock is released, the potential energy is converted into kinetic energy. The formula for kinetic energy is KE = (1/2) * m * v^2, where:
- KE is the kinetic energy,
- m is the mass of the rock (50 grams = 0.05 kg), and
- v is the velocity of the rock.

7. Substituting values and calculating:
- Using the given values, substitute m = 0.05 kg and x = 0.3 m into the potential energy equation from step 5 to calculate the energy (PE).
- Substitute m = 0.05 kg into the kinetic energy equation from step 6, and solve for v to find the velocity of the rock.

Remember to convert the units to SI units (meters and kilograms) if necessary before performing calculations.