How High Does a Rocket Climb After Fuel Depletion?

[kurosaki69]

Homework Statement

a rocket moves upward, starting from rest with an acceleration of +29.2 m/s^2 for 4 s. it runs out of fuel at the end of the 4 s and continues to move upward. how high does it rise?

Homework Equations

The Attempt at a Solution

i tried using the equation s=1/2at^2+v1t+s1. when i plug in the numbers i got 233.6 as a solution. when i check in the back off the book the answer was 941. Can someone please help point me in the right direction by telling me what i did wrong.

 

[LowlyPion]

Homework Statement

a rocket moves upward, starting from rest with an acceleration of +29.2 m/s^2 for 4 s. it runs out of fuel at the end of the 4 s and continues to move upward. how high does it rise?

Homework Equations

The Attempt at a Solution

i tried using the equation s=1/2at^2+v1t+s1. when i plug in the numbers i got 233.6 as a solution. when i check in the back off the book the answer was 941. Can someone please help point me in the right direction by telling me what i did wrong.

There are two phases to your problem. One the blastoff- acceleration phase. That lasts 4 seconds. Then there is the free body phase. It starts with the final velocity of the previous phase. How much higher does it go against gravity alone?

You calculated the height of acceleration phase.

Now calculate from how fast it was going how much higher it went.

 

[kurosaki69]

i'm sorry what do you mean when you said "How much higher does it go against gravity alone?"

 

[LowlyPion]

i'm sorry what do you mean when you said "How much higher does it go against gravity alone?"

When the rocket burns out, it has a pretty good velocity. And it's at 233.6 feet. and still climbing. That velocity is then decelerated by gravity.

At that velocity going up, then and gravity slowing it. how much further than 233.6 feet does it go?

When you get that number, add it to the 233.6 feet.

 

[kurosaki69]

so then my final velocity that i had calculated from the acceleration phase would replace my original initial velocity which as 0.

 

[LowlyPion]

so then my final velocity that i had calculated from the acceleration phase would replace my original initial velocity which as 0.

Yes. Exactly.

 

[kurosaki69]

does it matter if my final calculation is not the exact answer as the book's. when i had finished solving i got 938.5 instead of 941.

 

[LowlyPion]

does it matter if my final calculation is not the exact answer as the book's. when i had finished solving i got 938.5 instead of 941.

That looks like rounding error.

Does it matter?

Only your teacher knows for sure.

But if you understand it, that's worth more than a grade.

 

[kurosaki69]

well thank you for helping me.