Calculating Maximum Height and Flight Time of a Model Rocket Launch

[gadawg90]

A model rocket is launched straight upward with an initial speed of 54.4 m/s. It accelerates with a constant upward acceleration of 2.20 m/s2 until its engines stop at an altitude of 131 m. What is the maximum height reached by the rocket? How long after lift off does the rocket reach its maximum height? How long is the rocket in the air?

well i was thinking that the velocity final would be 0 since at the top it would stop for a very short time, so i plugged the numbers into the equation
Vf^2=Vi^2+2ad and solved for d, but that's not right.i got 673 m

 

[kuruman]

You need to do this in two parts. Don't forget that the rocket doesn't come to a dead stop once its engines stop running. The equation that you quoted can give you the speed of the rocket until its engines stop at an altitude of 131 m. Finding that speed is the first part. After that the rocket is in free fall, but climbs even higher. How much higher? That's the second part.

 

[gadawg90]

alright well i found the velocity final at 131 m to be 93.40 meters, so would i use the same equation and use that as my velocity initial and my velocity final be 0?

 

[kuruman]

Yes, the same equation, but with different acceleration, of course.

 

[gadawg90]

sorry, but would it turn into a free fall question and the acceleration be -9.8? i tried it and it was wrong..

 

[ideasrule]

sorry, but would it turn into a free fall question and the acceleration be -9.8? i tried it and it was wrong..

Yes, it turns into a freefall question. Can you post your solution? It shouldn't be wrong.

 

[gadawg90]

Alright so i set up the second equation like this
0=93.4^2 + 2(-9.8)d
and for d i got 445.08 m

 

[kuruman]

That looks about right. So what is the maximum height reached by the rocket?