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
