# Differential Equation of a model rocket

• aqmal_12
In summary, the conversation discusses a problem involving the acceleration of a model rocket, which is proportional to the difference between 100 ft/sec and the rocket's velocity. The initial acceleration is given as 50 ft/sec2 and the goal is to find the time it takes for the rocket to reach a velocity of 80 ft/s. The solution involves setting up a differential equation and using techniques to solve it.

## Homework Statement

Suppose that the acceleration of a model rocket is proportional to the difference between 100 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 50 ft/sec2, how long will it take to accelerate to 80 ft/s?

## The Attempt at a Solution

I've tried to solve like this.
Vi=0 a=50ft/s^2 Vf=80ft/s

a=k(100-v)
50=k(100-0)
k=0.5

Sorry but that's all I know. I'm new to this topic. I hope you can guide me. Thank you so much.

aqmal_12 said:

## Homework Statement

Suppose that the acceleration of a model rocket is proportional to the difference between 100 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 50 ft/sec2, how long will it take to accelerate to 80 ft/s?

## The Attempt at a Solution

I've tried to solve like this.
Vi=0 a=50ft/s^2 Vf=80ft/s

a=k(100-v)
50=k(100-0)
k=0.5

Sorry but that's all I know. I'm new to this topic. I hope you can guide me. Thank you so much.

Hello aqmal_12, welcome to PF. You have the k figured out but you need to get your differential equation written. Remember that acceleration and velocity can be expressed in terms of position s and its derivatives. So what does your equation

a = k(100-v)

become when you express it in terms of s and its derivatives? Once you have that written, you have to solve it using techniques you have learned so far.

## 1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It describes the relationship between the rate of change of a variable and the variable itself.

## 2. How is a differential equation used in a model rocket?

A differential equation is used in a model rocket to describe the motion of the rocket as it travels through the air. It takes into account factors such as air resistance, gravity, and thrust to determine the rocket's trajectory.

## 3. What is the significance of solving a differential equation for a model rocket?

Solving a differential equation for a model rocket allows us to accurately predict its flight path and ensure it reaches the intended destination. It also helps us understand the forces and factors that affect the rocket's motion.

## 4. How do the initial conditions affect the differential equation of a model rocket?

The initial conditions, such as the rocket's initial position and velocity, are used as starting points for solving the differential equation. They play a crucial role in determining the rocket's trajectory and must be carefully considered in the design and launch of the rocket.

## 5. Are there any limitations to using a differential equation for a model rocket?

While a differential equation provides a good approximation of a model rocket's motion, it does not account for all real-world factors such as wind, turbulence, and structural integrity. As such, it is important to use caution when relying solely on the results of a differential equation for a model rocket's flight.