Calculating Velocity, Max Height, and Impulse - Bottle Rocket Lab

[MacFanBoy]

Check my work please!

Homework Statement

given/known:
-mass of rocket 140.25g
-Gravity
-time 6.91s(up and down) -or- 3.46s (one direction)

Ideally, the rockets were supposed to go straight up and straight down, and even though this obviously didn't happen, we are assuming it did. It is assumed that the time of powered flight is essentially zero and that all of the water in the rocket was released instantly at lift-off, even though that is slightly unrealistic, to simplify the calculations, thus the only mass that needs to be considered is the mass of the rocket with no water inside. Apparently the launch also took place in an environment that has no wind resistance and ignores the rotation of the earth, and only the downward acceleration of gravity (-9.8 m/s) is taken into consideration.
Find the velocity, maximum height, and impulse (in Newton-seconds)

Homework Equations

what I used: h=.5gt² v=gt Impulse=Ft=mv

The Attempt at a Solution

h=.5(9.80m/s²)(3.46s)² = 58.66m

v=gt = (9.80m/s^2)(3.46s) = 33.91m/s

Impulse=Ft=mv= (.14025kg)(33.91m/s)=4.756N-sSo is all of that correct?

Thanks

Sorry if this is in the wrong section too. It's an AP Physics course so it is technically undergrad, but not 100% sure.

 

[Jhero]

Hello,

I have reviewed your work and I have some comments and suggestions for improvement.

Firstly, your calculation for the maximum height is correct, assuming that the rocket goes straight up and down and that the initial velocity is zero. However, it would be helpful to include units in your final answer, so the maximum height would be 58.66 meters.

Secondly, your calculation for the velocity is also correct, assuming that the initial velocity is zero. Again, it would be helpful to include units in your final answer, so the velocity would be 33.91 meters per second.

Finally, your calculation for the impulse is incorrect. The formula for impulse is FΔt, where F is the average force and Δt is the time interval over which the force is applied. In this case, the average force is the weight of the rocket, which is given by F=mg, where m is the mass of the rocket (140.25g) and g is the acceleration due to gravity (-9.8 m/s^2). So the impulse would be calculated as:

Impulse=FΔt=mgΔt= (0.14025kg)(9.8m/s^2)(6.91s)= 8.974N-s

Again, it would be helpful to include units in your final answer, so the impulse would be 8.974 Newton-seconds.

I hope this helps and good luck with your studies!