Rocket’s Red GlareA 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?

Project Overview

Product Testing Nerf Guns◦ Testing the claim on the box.

Engaging

How did I come up with the idea?

◦ Ownership belongs to the student.

Overview

N-Strike Elite Triad ex-3 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

Mathematics

Free Fall◦ Use The Physics Classroom-Free◦ Use Teachers Domain ( now PBS Learning) Free

Projectile motion & Kinematic Equations◦ Explore Learning Software- Not Free

Physics

Software : Explore Learning◦ www.Explorelearnig.com◦ Excellent for simulations where labs are not

available.◦ Can easily extend ideas- “what if”scenarios

Graphing Calculator◦ Parametric Mode

Technology

2)8.9(2

1)( ttH tVtx x)(

Equation1 : Equation 2:

Vx = V0cos(q) Where V0 = firing velocity and Vx = velocity in x direction.So when the angle is 0,

Vx = V0cos(0)Vx = V0(1)Vx = V0

Determine the Firing Velocity

H(t)= distance object falls X(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

You m

easu

re

Fire nerf gun horizontally

A little hot glue , string , weight and A protractor is all it takes!

Students should take severaltrials of data and average.

How We Tested the Claim

Time

H = ½(9.8)T²1.46=1/2(9.8)T²1.46 = 4.9T² 4.9 4.9 .297 = T² .545 s = T

This equation means that it took .545 seconds for the projectile to land after being fired.

Initial Velocity

V = D/TV = 9.79/.545V = 17.96 m/s

This equation means that the velocity of the projectile was 17.96 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.

 

)sin(

2

1)(

0

02

vv

HtvgttH

y

y

Calculations X= VoT

7.5M=Vo(.507)

14.793 Meters Per second

VY=VoSin45=14.793Sin(45)

Vx=VoCos45= 14.793Cos(45)

Calculations

H(T)=-1/2(9.8)T^2 + VYT + Ho

H(T)=-4.9T^2+10.46T+1.26

See graph for maximum height.

Max height = 6.84 meters = 22.35 feet

Calculations

Conclusion Our Nerf gun had max range of 22.35 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.

Resources NASA Rocket Sources

The Physics Classroom Elephant and Feather

Vernier Product- motion detectors