# What is the rocket's initial acceleration?

• JoeDGreat
JoeDGreat
New user has been reminded to always show their work when posting schoolwork questions
Homework Statement
A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s. What is the rocket's initial acceleration?
Relevant Equations
Vf-Vi = VeIn(Mi/Mf)
Help me solve... I'm getting errors here..

The rocket equation you have quoted is not very useful to find acceleration. For that you need to look at the fundamental conservation law that is behind the rocket equation, and specifically how the conserved quantities of the rocket and ejected propellant change the instant the rocket is turned on.

JoeDGreat said:
Homework Statement: A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s. What is the rocket's initial acceleration?
Relevant Equations: Vf-Vi = VeIn(Mi/Mf)

Help me solve... I'm getting errors here..

a = -Ve/Me × dM/dt
dM/dt = Mi/120 ÷ 1sec = -Mi/120sec
a =-2400/Mi ( -Mi/120) = 20m/s²

PS: This is the textbook solving but, I don't know how dM= Mi/120

JoeDGreat said:
a = -Ve/Me × dM/dt
dM/dt = Mi/120 ÷ 1sec = -Mi/120sec
a =-2400/Mi ( -Mi/120) = 20m/s²

PS: This is the textbook solving but, I don't know how dM= Mi/120
They are giving you the instantaneous rate of mass ejection at ##t=0##:

## \dot M(0) = -\frac{1}{120}M \frac{ \text{kg}}{ \text{s}} ##

Then apply "The Rocket Equation" at ##t = 0## (with no external forces).

Last edited:
JoeDGreat said:
In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s.
Is it this statement that is giving you interpretive issues? They should have just said something to the effect of " at the instant of firing", or we are just to assume the mass flow rate as constant over the first second for the sake of simplicity (i.e. being able to find a solution).

A loss of 1/120th of total mass is sufficiently small that we don't need to worry about how it changes over the second, or, indeed, that it changes at all. Just use momentum conservation: m/120 * 2400m/s = m*v.
Then a=v/t.

jbriggs444

## 1. What is initial acceleration?

Initial acceleration refers to the rate at which a rocket's velocity changes when it first begins its ascent into space. It is typically measured in meters per second squared (m/s^2).

## 2. How is initial acceleration calculated?

Initial acceleration can be calculated by dividing the change in velocity (measured in meters per second) by the change in time (measured in seconds). This can be represented by the formula a = Δv/Δt, where "a" represents initial acceleration, "Δv" represents change in velocity, and "Δt" represents change in time.

## 3. What factors affect a rocket's initial acceleration?

The initial acceleration of a rocket is affected by several factors, including the thrust of the rocket's engines, the mass of the rocket, and the force of gravity acting upon the rocket.

## 4. Why is initial acceleration important in rocket launches?

Initial acceleration is important in rocket launches because it determines how quickly the rocket can gain altitude and reach its desired destination. A higher initial acceleration allows the rocket to reach higher speeds and achieve escape velocity, which is necessary for leaving Earth's atmosphere and entering space.

## 5. Can initial acceleration change during a rocket's flight?

Yes, initial acceleration can change during a rocket's flight. As the rocket expends fuel and becomes lighter, its initial acceleration may increase. Additionally, the force of gravity acting upon the rocket may also change as it travels further away from Earth's surface, affecting its initial acceleration.

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