To find the maximum velocity of the rocket, you can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time taken. In this case, t would be 3.48 seconds and a would be the acceleration due to gravity, which is approximately 9.8 m/s^2. So, the maximum velocity would be v = 0 + (9.8)(3.48) = 34.104 m/s.
To calculate the average thrust, you can use the equation F = m x a, where F is the force (thrust), m is the mass of the rocket, and a is the acceleration. You would need to know the mass of the rocket and the acceleration it experiences during the launch. This information is usually provided by the rocket manufacturer. Once you have the force, you can divide it by the time taken (3.48 seconds) to get the average thrust.
To find the energy stored in the engine, you can use the equation E = 1/2 x m x v^2, where E is the energy, m is the mass of the rocket, and v is the velocity. In this case, you would use the maximum velocity you calculated earlier. Again, you would need to know the mass of the rocket, which can be obtained from the manufacturer.
Finally, to calculate the time taken to reach maximum height, you can use the equation h = ut + 1/2 x a x t^2, where h is the maximum height, u is the initial velocity (which is 0), a is the acceleration due to gravity, and t is the time taken. In this case, you would use the maximum height of 99m and solve for t. It is important to note that this equation assumes that there is no air resistance, so the actual time taken may be slightly different.
I hope these hints and equations help you in your calculations. Remember to always double check your units and make sure they are consistent. Good luck with your rocket launch!
