Archived What angle maximizes the horizontal distance of a rocket launch?

[RobertL]

Hey everyone,

I've been trying to do a problem in which I attempt to find the angle that maximizes the horizontal distance of a rocket, which has a stage with thrust and then a stage as a projectile. After a delay period, an ejection charge fires and causes the rocket to drop straight down. I want to have the ejection charge to fire before the rocket hits the ground, which means giving a bit of leeway.

If any of you can look over my work and give me any suggestions, I would greatly appreciate it.

Homework Statement

Thrust: 3.42 N
Burn Time (constant thrust assumed): .33s
Delay time before ejection charge fires after burn time: 1.74s
Mass: .033893kg

Other values are calculated in the spreadsheet.

Homework Equations

Equations of motion/projectiles

The Attempt at a Solution

See spreadsheet. In it, I attempted to use the goal seek function to set the total time since burnout equal to the delay time (1.74s) by changing the value of the angle.

Thanks for any ideas!

 

[mfb]

The maximal distance will be reached if the rocket is just above the ground after 1.74 seconds. Safety factors can be added as necessary. Assuming a constant thrust vector, this leads to a quadratic equation for the vertical acceleration, which can be solved analytically.