Analyzing Firing Velocity of N-Strike Elite Nerf Gun by Haley Vermette
Haley Vermette conducted a project to test the claim made by Hasbro about the N-Strike Elite Nerf Gun's shooting range. Through critical thinking, problem-solving, and testing, various variables like time, distance, muzzle height, and firing velocity were analyzed to support or disprove the claim on the toy's box. The project involved detailed procedures, calculations, and the determination of the firing velocity to ensure accuracy. Data collection, equations, and height calculations were integral parts of the project to assess the toy's performance.
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Presentation Transcript
Test the Claim By Haley Vermette
Whats their claim? The Hasbro company that produced the N-Strike Elite Nerf Gun claimed that their toy could shoot 75 ft.
Overview Throughout this project we had to use critical and creative thinking. We also had to use problem solving in order to complete the task. We had to perform a series of tests and complete a series of equations to support that the claim on the front of the box is true.
Variables Independent Variables -Time Dependent Variables -Distance the bullet traveled (horizontal distance) -Height of the muzzle -Height of the bullet in the air (at any time) -Maximum height of the bullet -Firing Angle -Firing Velocity -Velocity in the vertical -Velocity in the horizontal
Determine the Firing Velocity: Set launch angle to zero degrees. This makes the horizontal component of the velocity in the x- direction. Using the equation Vx=V0cos(?) When an object is dropped from a height of H, the time it takes to hit the ground is the same when it is fired or launched from the gun at the same height and angle of zero degrees. Where Vx equals the velocity in the x-direction and V0equals the initial velocity when when the angle is 0 .
The Procedure Trial X(t) 1 295 in 1. Tape gun to desk and make sure the gun is angled at 0 2 311 in 2. Shoot one bullet and mark how far it went 3 307 in 3. Repeat step 2 5 or more times 4 312 in 5 341 in 4. Record all data 5. Take average of all the distances Average distance: 257.2 inches or 21.433 feet Height of muzzle: 2.5 feet
Calculations Equation 1: Time to hit the ground Equation 2: Firing velocity H(t)= (32)t2 X(t)=V0t
Calculating the Height of the Projectile Equation: H(t)= gt2+ vy t + H0 Once you have all the data you can fill in the equation and it will look like: H(t) = height at any time of the projectile H(t)= -16t2 + 38.3t + 2 g= gravity (-32 f/s/s) Which can then be plugged into the graphing function of your calculator. Once this is done you can find the maximum height of your projectile. You can also calculate the time it took to hit the ground. t= time in seconds of entire flight V0= Initial velocity Vy= Vertical component of velocity using the equation: Vy= V0sin(?) We found our maximum height to be 24.9 ft at approximately 1.19 seconds. H0= Height of nerf gun initially It took approximately 2.4 seconds for the bullet to hit the ground.
Vertex or H(t) = 24.92 Using Desmos Using the desmos graphing calculator I was able to graph the equation of the height of the projectile. By doing this I could see the complete behavior of the projectile from beginning to end. X-int = 2.445 seconds
Calculate the Horizontal Position x(t)= vx t Calculations: t= time in the air x(t)= vx t v0= initial velocity x(t)= (38.32519)(2.448773) ?= firing angle x(t)= 93.84968 vx= horizontal component of the velocity using the equation vx= v0cos(?) The bullet could fire approximately 94 feet.
In these images you can see how much drag effects the distance of the bullet. Although this is just an online exercise it is very effective in showing that drag depletes the distance the bullet will go. Air Resistance No Air Resistance
Conclusion: Is the claim right? The claim was that the N-Strike Elite could fire a nerf bullet 75 feet. Our final result was that the N-Strike Elite could fire a nerf bullet approximately 94 feet with no drag calculated. We do not know how the nerf company came up with their claim of how far the nerf bullet would shoot. This is an estimate that is reasonable when the gun is angled at 45 with no drag. The data we collected is unreasonable in the vertical but, reasonable in the horizontal. The answer calculated is most likely correct and reasonable if it were recalculated with the air resistance and drag.
Reflection Overall this year has been really great, I have learned so many new concepts in math that I would ve never learned in a typical classroom setting. I loved how everything was very hands on and we applied all our math skills to real life scenarios. I also liked how we took our time getting to know the material and made sure everyone in the class understood what was going on before we moved on. Dropping spanish to take math modeling was definitely a great idea! Thanks for a great year Mrs. Falk!
