Help! Physics Problem: Find Theta for 1000m Target

[Feeb]

http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4836&context=ujmm

Ive been awake for thirty six hours and I don't know differential equations.

Im trying to find the angle (theta) over the horizontal axis that is needed to hit a target that is 1000 meters away
they are basically identical problems. I don't understand how to find initial velocity in the x and y components if I don't have an angle. Is there a final formula I can plug and chug to find theta?

I am working on a problem for my calculus that is exactly like this, but I can't figure out how she arrived to her answer my grade depends heavily on this.

 

[Bystander]

You've given us one problem. What's the other?

 

[Vivek des]

If you have the magnitude of initial velocity in which it should be project you can solve this..

 

[Feeb]

Lets just say that the velocity was 820 m/s at. Ignoring the fact that projectiles act differently at supersonic speeds, and accounting for a -kv^2 kind of relationship, how would I find theta?

 

[Vivek des]

For a projectile from ground with an angle θ The horizontal range is v^2sin2θ/g... Equate this to the distant target which the projectile should hit.. You will get the value of θ .. That's it ..

 

[Feeb]

I don't know how to evaluate all of that is the problem

 

[SteamKing]

http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=4836&context=ujmm

Ive been awake for thirty six hours and I don't know differential equations.

Im trying to find the angle (theta) over the horizontal axis that is needed to hit a target that is 1000 meters away
they are basically identical problems. I don't understand how to find initial velocity in the x and y components if I don't have an angle. Is there a final formula I can plug and chug to find theta?

I am working on a problem for my calculus that is exactly like this, but I can't figure out how she arrived to her answer my grade depends heavily on this.

The author has set up a spreadsheet to do the calculations to solve her problem. She can input various angles and have the spreadsheet calculate the properties of the resulting trajectory. It's a simple matter of assuming an angle, checking to see if the bullet arrives at the target location, and then adjusting the angle up or down as required.

If you read the author's write up, she initially thought the rifle would have to be fired at an angle of elevation of 30° in order to hit the target. Her calculations showed that a much smaller angle of elevation, less than half a degree, was sufficient.

If you've been up 36 hours, get some sleep. Your brain is fried and you won't find any inspiration without getting some rest.

 

[Feeb]

I don't have a choice in sleeping, its due soon. The whole point of this project is to take the guesswork out of problems and show that it can be solved through the rigorous application of mathematics. That being said I guess that is the very nature of using the Euler Method

 

[Delphi51]

These models can be fun. No calculus needed. The idea is to calculate the forces on the bullet immediately after leaving the gun (time 0). Use your basic formulas for uniform accelerated motion to find what those forces do to the velocity and position over a small time interval. This gives you the position and velocity for the next row of your spreadsheet - so you can use the same formulas to do the next time interval. You might begin your solution by ignoring the horizontal motion and just do the vertical, as if the bullet was just dropped. Easy to check and see if the spreadsheet produces the correct answer! Have a go at the first time interval and we will be happy to check it for you.