How Is the Quadratic Formula Used in Engineering and Physics?

[MacLaddy]

Homework Statement

The Quadratic Equation. I am looking for an example of the quadratic equation being used in any form of engineering, or physics.

I am supposed to give an example for my algebra class, but I really don't want to do the "two trains left a station," or "sally jumped off a log."

I don't know if there are ANY applications of this in engineering or physics that I could use, as it needs to be basic algebra, but I am hoping.

Maybe something simple like $$f(w) = 10w^2 + 5x + 25 = 0$$, where w is windspeed, and the function is for how many turns an hour a windmill will get... Not sure if something like that exists.

My class will let me use an existing formula, or to create an example.

Homework Equations

$$ax^2 + bx + c = 0$$

The Attempt at a Solution

Searching, googling, pacing, and asking here.

I appreciate any assistance that can be offered.

 

[LCKurtz]

How about an artillery shot problem. Given muzzle velocity what elevation angle to hit a target. When will it hit the ground? Uses

s = (-1/2)gt²+v₀t+s₀

 

[MacLaddy]

I would love to be able to use something like that, but what I mean when I say "basic algebra" is because I honestly can't solve that yet... (sadly) I guess I'll get there soon.

I know that is pronounced v-naught, but I don't know what it means.

I appreciate the effort, but perhaps can you give me a simpler explanation? (algebra 101 level)

 

[LCKurtz]

How about an artillery shot problem. Given muzzle velocity what elevation angle to hit a target. When will it hit the ground? Uses

s = (-1/2)gt²+v₀t+s₀

I would love to be able to use something like that, but what I mean when I say "basic algebra" is because I honestly can't solve that yet... (sadly) I guess I'll get there soon.

I know that is pronounced v-naught, but I don't know what it means.

I appreciate the effort, but perhaps can you give me a simpler explanation? (algebra 101 level)

Make it simpler. The equation I gave is for a body falling under the influence of gravity. g = 32 ft/sec², s₀ is the initial position, v₀ is the initial velocity. You could examine the following proposition:

Someone claimed that Michael Jordon could jump high enough that he had a 3 second hang time. How high would he have to jump to do that? The equation you need to answer that is

s = (-1/2)gt²+v₀t+s₀

where s is the height at time t. Start the jump with s₀ = 0 at time t = 0 and unknown v₀. You need some algebra to find the vertex of the (s,t) parabola and relate it to hitting the ground 3 seconds later.