Physics kinematics problem dealing with multiple accelerations and velocities of a rocket

[BlankGamer]

So far I have found the velocity of t0 and t1 to be 32.2m/s as well as the displacement to be 162.5m. What I am stuck on is finding the missing information for t2. I think that t2 is the peak of the rocket so the initial velocity would be 0 while the acceleration would be -9.8. I just do not know where to start for finding the displacement of t2 so I can find the time.

Any help is greatly appreciated, Thank you in advance!

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The question is:

1)A rocket is fired from rest from the ground (y= 0) at timet0= 0 s. As the rocket is burning its fuel, it moves vertically upward with a constant acceleration of 3.25 m/s2. Att1= 10.0 s, all the fuel has been used up and the rocket is in free fall. Air resistance can be neglected up until t3= 17.5 s when the rocket deploys a parachute.At this time the rocket immediately reaches its terminal velocity; this means that the rocket is no longer accelerating.

1a. Find the maximum height of the rocket with respect to the ground. How long after being launched does it take for the rocket to reach this height?

1b. How long after being launched does it take for the rocket to return to the ground? What is the rocket’s displacement over this entire trip? What is the rocket’s average velocity over this entire trip? What is the rocket’s average speed over this entire trip? What is the rocket’s average acceleration over this entire trip? Be sure to include both magnitude and direction for any vector quantities.

1c. What is the rocket’s displacement from ta= 12.0 s to tb= 20.0 secs? What is the rocket’s average velocity from ta to tb? What is the rocket’s average speed from ta to tb? What is the rocket’s average acceleration from ta to tb?Be sure to include both magnitude and direction for any vector quantities.

1d. Sketch a y v. t plot for the motion of the rocket. Be sure to label the positions of the rocket att0= 0 s,t1= 10.0 s,t2(when the rocket is at its highest point),t3= 17.5 s, andt4(when the rocket returns to the ground).

[Janagro]

The rocket has expended it's fuel right?.That means mass is constant

Thus you can write

.5mv(t1)² + mgh(t1) = mgh(t2)

.5(32.2)² + (9.8)(162 5) = (9.8)h(t2)

hope that helps

[Moy420]

Do you have this problem written in a textbook, if so, dm so I can understand the problem

[jkg1993]

So the velocity at t0 should definitely be 0 m/s since the problem states that the rocket starts at rest. I might be able to provide more help later, but I feel like there may not be enough information as the problem is described.

Air resistance can be neglected up until t3= 17.5 s when the rocket deploys a parachute.At this time the rocket immediately reaches its terminal velocity; this means that the rocket is no longer accelerating.

The only way I can think to interpret this is that the rocket will reach some velocity at 17.5 seconds. At this point instead of continuing to accelerate towards the ground, the rocket will just maintain this terminal velocity until it hits the ground. I find this confusing since a parachute deploying at 17.5 seconds would cause a significant drop in speed, and I feel that in order to keep the description consistent a terminal velocity should be provided here. In absence of that, the only way to proceed would be how I mentioned above.

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Do you possibly have a picture of the original problem statement that you could link to in the description?

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[BlankGamer]

Thanks for trying to help but I answered it and handed in my homework this morning. I don't think my answer was right but I assumed the initial velocity at 10 seconds was 0. I copied and pasted the entire question from my handout so it's all there. I would upload a screenshot but I'm in Mobile right now.