## Yahoo! 3 years ago 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

1. siddhantsharan

Okay. This is going to take some time. First we find the time. |dw:1347968161543:dw|

2. siddhantsharan

Now, $-100 = (150\sin \theta)t - 5t^2$ $t^2 - 30\sin \theta t -20=0$ Solving for t, $t = [30\sin \theta \pm \sqrt{(900\sin^2 \theta) + 80}]/2$

3. siddhantsharan

Now , We need to find the expression for range. $Range = (150\cos \theta)*t$

4. siddhantsharan

5. siddhantsharan

To maximize differenciate R with respect to theta.

6. siddhantsharan

@Yahoo! Calculation is there. But other than that, Do you get it?

7. Yahoo!

Yup....i understood...ur method.....Does...This...need...Serious....Calculus...Since....i am ..not very much exp with it...

8. siddhantsharan

No. Not really. You know product rule, right?

9. siddhantsharan

You should get a value close to 45 degrees. Maybe something like 43 degrees or 44.

10. Yahoo!

Yup..it shuld be 43.75

11. siddhantsharan

Yeah. :)

12. Yahoo!

thxxx