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.

 

[DeeNos]

One example of the quadratic formula being used in engineering is in calculating the trajectory of a projectile. The quadratic formula can be used to solve for the maximum height, range, and time of flight of a projectile launched at a certain angle and velocity. This information is important in designing and predicting the path of a projectile, such as a rocket or a cannonball.

Another example is in calculating the optimal angle for a ramp or slope. The quadratic formula can be used to determine the angle at which an object will have the maximum speed or distance when sliding down a slope, such as in a roller coaster or a ski jump.

In physics, the quadratic formula is used in solving problems involving motion and acceleration. For example, it can be used to calculate the time it takes for an object to reach a certain speed or distance, or to determine the maximum height a ball will bounce when dropped from a certain height.

In engineering, the quadratic formula is also used in designing and analyzing circuits. It can be used to solve for the voltage or current in a circuit, as well as to determine the resonant frequency of an electrical circuit.

Overall, the quadratic formula is an important tool in mathematics and has numerous applications in engineering and physics. Its ability to solve for unknown variables in a wide range of problems makes it a valuable tool for scientists and engineers.