# Acceleration due to gravity of a rocket

## Main Question or Discussion Point

If an object say a rocket is thrown up in the sky with an additional acceleration say ' x ' , then why do we add the value of acceleration due to gravity i.e 9.8 m/s^2 to the acceleration ' x' in order to find the total acceleration.......
Since vector of acceleration due to gravity is directed downwards...so we consider it - 9.8 m/s^2 . So in accordance to this, if we find total acceleration then we should subtract 9.8 m/s^2 from 'x ' m/s^2 because...firstly, gravity is -9.8 m/s^2 and secondly, acceleration due to gravity will constantly decrease if the rocket or object will continue going up int he sky with that X acceleration. So why should 9.8 m/s^2 be added to X m/s^2 and not subtracted ?

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Bandersnatch
If you add a negative value you're subtracting it, no?
$a+(-b)=a-b$

If you add a negative value you're subtracting it, no?
$a+(-b)=a-b$

But as the bookish explanation says, we add the positive value of acceleration due to gravity and not the negative one....
That's why I am confused...
Need some help and guidance

Bandersnatch
That doesn't seem right. Can you provide more context for the question? Perhaps a verbatim description of the problem as stated in your book? (a picture will do)

That doesn't seem right. Can you provide more context for the question? Perhaps a verbatim description of the problem as stated in your book? (a picture will do)

The example goes on like this :

A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m/s^2 . Find the initial thrust(force) of the blast.
Take g=9.8 m/s^2

Solution (as given in my book) :
The rocket moves up against gravity with an acceleration of 5.0 m/s^2 .
Hence the blast produces a total acceleration of =
a=9.8+ 5.0 =14.8 m/s^2
By Newton's II law, the initial thrust(force) of the blast is =
F=ma = 20,000 kg x 14.8 m/s^2 =2.96 x 10^5 N.
Therefore, answer is 2.96 x 10^5 N

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The example goes on like this :

A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m/s^2 . Find the initial thrust(force) of the blast.
Take g=9.8 m/s^2

Solution (as given in my book) :
The rocket moves up against gravity with an acceleration of 5.0 m/s^2 .
Hence the blast produces a total acceleration of =
a=9.8+ 5.0 =14.8 m/s^2
By Newton's II law, the initial thrust(force) of the blast is =
F=ma = 20,000 kg x 14.8 m/s^2 =2.96 x 10^5 N.

My doubt is the underlined portion only. If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?????

Bandersnatch
That could be written more clearly to show what's going on.

Try this:
$a=g+t$
where a is the net acceleration (5m/s^2, positive is up), g is the gravitational acceleration (-9.8m/s^2) and t is the thrust you want to find. Here, the signs show you the directions of the vectors.

If you rearrange the above to solve for t, you get the equation in your book.
The book simply went straight for the rearranged equation.

Note that the acceleration due to gravity is not
but is deducted from the net (initial) acceleration. $-(-9.8) = +9.8$

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A.T.
My doubt is the underlined portion only. If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?????
To get the proper acceleration, relative to free fall. That's what the engine must provide to cancel gravity and accelerate up.

That could be written more clearly to show what's going on.

Try this:
$a=g+t$
where a is the net acceleration (5m/s^2, positive is up), g is the gravitational acceleration (-9.8m/s^2) and t is the thrust you want to find. Here, the signs show you the directions of the vectors.

If you rearrange the above to solve for t, you get the equation in your book.
The book simply went straight for the rearranged equation.

Not that the acceleration due to gravity is not

but is deducted from the net (initial) acceleration. $-(-9.8) = +9.8$

Oh....THANKYOU soooooooooooooooo much....
I got it!
I can now see it clearly....yaa......I've undersood it now....
Once again...THANKS A LOT !
It was really very sweet of you to guide me .....
Gratitude.

Chestermiller
Mentor
5 - (-9.8)=14.8

Chet

5 - (-9.8)=14.8

Chet

Thank you so much .. Sir....
I got it !...
It was really simple and I was stuck at it like anything...
Thank you so much for helping me out.

Chestermiller
Mentor
Thank you so much .. Sir....
I got it !...
It was really simple and I was stuck at it like anything...
Thank you so much for helping me out.
It would have been much easier if you had drawn a free body diagram of the rocket, and then, based on the free body diagram, written the force balance:

F - mg = ma

Chet

CWatters
Homework Helper
Gold Member
If the rocket moves against gravity then why should acceleration due to gravity be added to the initial acceleration?????
Perhaps think like this...

How much thrust would the rocket have to produce so that it only just manages to lift off the ground without accelerating upwards?

Then how much more does it have to produce to accelerate upwards at "a"?

What's the total?