A project to model product testing

 A project in studying motion in two dimensions.  Applying Polynomials to REAL-World problems  How can we use mathematics to test products?

 Product Testing Nerf Guns ◦ Testing the claim on the box.  Engaging  How did I come up with the idea? ◦ Ownership belongs to the student.

 Holds 3 darts  Pull back cocking handle to get ready to fire the shot  Shoots the barrel that is loaded, but not all at the same time  ‘Shoots up to 75 feet / 20 meters’

 Polynomials  Translating Functions ◦ F(x) = a(x-h) 2 +k ◦ F(x)= a(x-h) 3 +k  Parametric Functions  Trigonometry  Geometry

 Free Fall ◦ Use The Physics Classroom-Free ◦ Use Teachers Domain ( now PBS Learning) Free  Projectile motion & Kinematic Equations ◦ Explore Learning Software- Not Free

 Software : Explore Learning ◦ ◦ Excellent for simulations where labs are not available. ◦ Can easily extend ideas- “what if”scenarios  Graphing Calculator ◦ Parametric Mode

Equation1 : Equation 2: V x = V 0 cos  ) Where V 0 = firing velocity and V x = velocity in x direction. So when the angle is 0, V x = V 0 cos(0) V x = V 0 (1) V x = V 0 Determine the Firing Velocity H(t)= distance object fallsX(t)= distance along ground

X(t) H(t) The time it takes the projectile to hit the ground will be Found by using H(t). Use the “time” found in x(t) to Determine the firing velocity. You measure Fire nerf gun horizontally

A little hot glue, string, weight and A protractor is all it takes! Students should take several trials of data and average.

Time  H = ½(9.8)T² 1.46=1/2(9.8)T² 1.46 = 4.9T² = T².545 s = T  This equation means that it took.545 seconds for the projectile to land after being fired. Initial Velocity  V = D/T V = 9.79/.545 V = m/s  This equation means that the velocity of the projectile was meters per second.

Calculate Height of Nerf Projectile 2 Method Method I: Use equations from Physics. Use the following equations to determine the height, H, of the projectile at any time, t. Your resulting equation will be in terms of H and t.

 X= V o T  7.5M=V o (.507)  Meters Per second  V Y =V o Sin45=14.793Sin(45)  V x =V o Cos45= Cos(45)

 H(T)=-1/2(9.8)T^2 + V Y T + H o  H(T)=-4.9T^ T+1.26  See graph for maximum height.  Max height = 6.84 meters = feet

 Our Nerf gun had max range of feet. The claim on the box was 35 feet. Out gun shot below the claim. Our equations are probably an underestimate since we did not include drag. Its difficult to verify the claim but it is probably not accurate.

 NASA Rocket Sources NASA Rocket Sources  The Physics Classroom The Physics Classroom  Elephant and Feather Elephant and Feather  Vernier Product- motion detectors