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Yahoo!
A machine gun is mounted on the top of tower 100m high.At what angle should the gun be inclined to cover a max range of firing the ground below?Muzzle speed=150m/s,take g=10m/s^2
Okay. This is going to take some time. First we find the time. |dw:1347968161543:dw|
Now, \[-100 = (150\sin \theta)t - 5t^2\] \[t^2 - 30\sin \theta t -20=0\] Solving for t, \[t = [30\sin \theta \pm \sqrt{(900\sin^2 \theta) + 80}]/2\]
Now , We need to find the expression for range. \[Range = (150\cos \theta)*t\]
Substituting t and maximizing your expression will give you the answer.
To maximize differenciate R with respect to theta.
@Yahoo! Calculation is there. But other than that, Do you get it?
Yup....i understood...ur method.....Does...This...need...Serious....Calculus...Since....i am ..not very much exp with it...
No. Not really. You know product rule, right?
You should get a value close to 45 degrees. Maybe something like 43 degrees or 44.