I'm not sure how to address any of these. I"ve attempted them but each time I do, I've gotten different answers. I'm not even sure where to begin.
1. The Duke’s efforts to conquer the Count are starting to really falter. He has been forced back away from the walls quite a bit because his weaponry isn’t as effective. He decides to unleash his most powerful weapon, a huge catapult (double the range, in theory, of normal catapults) and fire it at the Count’s castle. The catapult is fired from 1.000km away at the same exact altitude as the count’s wall. The stone (mass of 1576.3 kg) is perfectly round and has a diameter of 1.500m. The duke carefully calculates the angle of fire for his catapult and fires. If he used an
angle of 35 degrees (which according to his calculations, should hit) he comes up short. How short does he end up (hint: figure out why he came up short)? (The drag coefficient can be assumed to be 0.5)
vt=sqrt(2mg/DpA)= sqrt(2(1576.3)(9.81)/.5(1.276)(1.767)= 165.586
vt=mg/b; b=mg/vt; 93.387
165.586/y=cos(theata); 165.586/cos(35)=
202.14.
What would be the units on this?
4. The duke used weak hinges to fasten the doors of the gate to the walls of the camp. If a force of 25N will dislodge each hinge (there are 4 of them) and the device (essentially a pendulum) is dropped 3.45m (from highest point when it is pulled back to the point it hits the door), how fast is the door moving when it breaks free?
I don't know how to even begin this.