Objectives

- Find out how far a projectile goes horizontally, given the height of the launcher, launch angle, and initial speed.
- Create your own problem with a unique set of conditions and solve for a different unknown variable.
- Develop procedures to solve problems with different unknown variables.

Ignore air resistance in the simulation.

Part 1 (Finding horizontal distance with given height, initial speed, and launch angle)

- Make a problem by setting the initial speed, launch angle, and launcher height to specific values. Ensure the object stays on the screen.
- Write a step-by-step process to calculate the horizontal distance (hint: start by finding the time in flight using a kinematic equation and watch out for signs).
- Solve your problem and verify the answer using the simulation for accuracy.

Part 2 (Solve for a different unknown variable)

- Explore the simulation to see what other variables can be solved for, given certain initial conditions. Pick a variable other than horizontal distance.
- Create a problem with the minimum initial conditions needed to solve for your chosen variable.
- Write down the steps needed to solve your problem.
- Solve your problem and verify the answer using the simulation for accuracy.

Part 3 (Writing procedures)

- Think of three different unknown variables you could solve for, given specific initial conditions.
- For each of the three unknown variables, write down the steps needed to solve for that variable. You don’t need to solve the problems, just write the steps.
- Make sure to label your initial conditions and the variable you’re solving for clearly in each procedure.

## Example

Let’s create an example for Part 1, where we find the horizontal distance a projectile will travel given the height of the launcher, the launch angle, and the initial speed.

Problem:

- Initial speed (Vo): 10 m/s
- Launch angle (θ): 30 degrees
- Height of the launcher (h): 5 meters

Step 1: Convert the launch angle to radians:

θ_rad = θ × (π/180)

= 30 × (π/180)

= π/6 radians

Step 2: Calculate the horizontal (Vox) and vertical (Voy) components of the initial velocity: Vox = Vo × cos(θ_rad)

= 10 × cos(π/6)

≈ 8.66 m/s

Voy = Vo × sin(θ_rad)

= 10 × sin(π/6)

≈ 5 m/s

Step 3: Find the time in flight for the projectile to reach the ground: We can use the kinematic equation:

h = Voy × t – 0.5 × g × t^2

Rearranging the equation to solve for time (t):

t = (Voy ± √(Voy² + 2 × g × h)) / g

Plugging in the values:

t = (5 ± √(5² + 2 × 9.81 × 5)) / 9.81

t ≈ 1.64 seconds (time in flight)

Step 4: Calculate the horizontal distance traveled (range):

Range = Vox × t

= 8.66 × 1.64

≈ 14.21 meters