Projectile Motion: Water Balloon Launch Project

[jrocco]

For a water balloon launch project, our students need to calculate the distance that the balloon will travel given the following information:

K- the spring constant of the launcher
the mass of the water balloon
the angle of launch
the distance that the launcher is pulled back.

Can anyone provide the sequence of equations (step by step) that leads to the students determining the distance that the balloon will travel?

I simply want them to tell me where to sit and they will launch their balloon (given the conditions above) and hopefully hit me.

Thanks

 

[berkeman]

For a water balloon launch project, our students need to calculate the distance that the balloon will travel given the following information:

K- the spring constant of the launcher
the mass of the water balloon
the angle of launch
the distance that the launcher is pulled back.

Can anyone provide the sequence of equations (step by step) that leads to the students determining the distance that the balloon will travel?

I simply want them to tell me where to sit and they will launch their balloon (given the conditions above) and hopefully hit me.

Thanks

Welcome to the PF.

I would think that you would want them to miss you, not hit you...

Are you familiar with the kinematic equations of motion for constant acceleration (the acceleration due to gravity in this case)?

http://en.wikipedia.org/wiki/Kinematics#Kinematics_of_constant_acceleration

.

 

[da_nang]

I'd first use the conservation of energy to calculate the initial velocity of the balloon once it's launched. Namely, potential energy in the spring becomes kinetic energy, if all other energy transformations are negligible. After that, do what berkeman said.

 

[jrocco]

I am slightly familiar with the kinematic equations. I do understand that in finding the initial velocity I use, v = squ 2(g)(h).

I am however looking for a simplified sequence of equations to givemy students. This is for a forensic science lesson related to ballistics.

So, if a student chooses to pull back the launcher 2 meters, launches a balloon with the mass of .234 kg at a 50 degree angle...how far will the balloon travel?

Thanks

 

[rwisz]

I would first suggest that the students gather all the necessary information and materials for the project, including the spring constant of the launcher, the mass of the water balloon, the angle of launch, and the distance that the launcher is pulled back. It is important to have accurate and precise measurements in order to obtain accurate results.

Next, the students can use the equations of projectile motion to calculate the distance that the balloon will travel. The first step would be to break down the initial velocity of the balloon into its horizontal and vertical components. This can be done using the angle of launch and the initial velocity of the balloon.

The horizontal component of the initial velocity can be calculated using the equation Vx = Vcosθ, where Vx is the horizontal component of the velocity and θ is the angle of launch. Similarly, the vertical component of the initial velocity can be calculated using the equation Vy = Vsinθ, where Vy is the vertical component of the velocity and θ is the angle of launch.

Next, the students can use the equation of motion for projectile motion, which is d = Vx*t, where d is the distance traveled, Vx is the horizontal component of the initial velocity, and t is the time of flight. The time of flight can be calculated using the equation t = 2*Vy/g, where g is the acceleration due to gravity (9.8 m/s^2).

Once the students have calculated the time of flight, they can plug it into the equation d = Vx*t to determine the distance that the balloon will travel. It is important to note that the distance calculated using this equation is the horizontal distance traveled by the balloon. If the students are interested in calculating the total distance traveled by the balloon, they can use the equation h = Vy*t - 1/2*g*t^2, where h is the maximum height reached by the balloon.

Finally, I would recommend that the students perform multiple trials and take the average of their results to ensure accuracy. They can also vary the angle of launch and the distance that the launcher is pulled back to see how it affects the distance traveled by the balloon.

I hope this helps in guiding the students towards determining the distance that the balloon will travel for their project. Happy experimenting!