# Constant acceleration simultaneous equation

• bigjuicy
In summary, two pizzas, one dropped from a height of 20m and the other thrown up at 30m/s from 0m, will meet at a position in the air where the two equations, x=0-1/2at^2 and x=30-1/2at^2, are equal. This requires solving a simultaneous equation with the variable t, which can then be used to determine the position x where the pizzas will meet.
bigjuicy

## Homework Statement

A pizza is being dropped from a height of 20 m. Another pizza is being thrown up at 30m/s from 0m(the one falling is above the one being thrown). At what position in the air will they meet?

a= -10m/s^2

## Homework Equations

Im not sure but i think that some of the b5 kinematics equations would apply. I am pretty sure that this requires a simultaneous equation.

## The Attempt at a Solution

i attempted to get all the t's to one side but got stuck at (2x/vi)/a=(t^2)/vi)+2t/a

i assumed that the t's must be equal. I am unsure whether or not i approached the problem correctly or not

I appreciate you guys for looking at this but i think i got it:
so basically

you have two side

first equation = falling pizza:

x=0-1/2at^2

you set that one, equal to your thrown pizza: x=30-1/2at^2

set them equal to each other, then solve for t then use that t to solve for x

## 1. What is constant acceleration simultaneous equation?

Constant acceleration simultaneous equation is a mathematical concept used to describe motion with a constant acceleration. It involves solving two simultaneous equations to find the values of time and displacement at any given point in time.

## 2. How is constant acceleration simultaneous equation derived?

The constant acceleration simultaneous equation is derived from the equations of motion, specifically the equations for displacement and velocity with constant acceleration. By setting these equations equal to each other and solving simultaneously, we can find the values of time and displacement.

## 3. What is the difference between constant acceleration and constant velocity?

Constant acceleration refers to a change in velocity over time, while constant velocity means there is no change in velocity. In other words, an object with constant acceleration will be speeding up or slowing down, while an object with constant velocity will maintain the same speed and direction.

## 4. How is the constant acceleration simultaneous equation used in real-life situations?

The constant acceleration simultaneous equation is commonly used in physics and engineering to analyze the motion of objects, such as projectiles, cars, and airplanes. It can also be applied in fields like economics and finance to model the growth or decline of investments.

## 5. Are there any limitations to using the constant acceleration simultaneous equation?

The constant acceleration simultaneous equation assumes that the acceleration remains constant throughout the motion, which may not always be the case in real life. It also does not take into account external factors such as air resistance, which can affect the accuracy of the results. Additionally, it is only applicable to objects moving in a straight line with constant acceleration.

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