What is the optimal angle to set a catapult for attacking a medieval city?

In summary, the commander of an attacking army in a medieval city with walls of length 550 m and height 16 m is planning to set fire to the city using a catapult. The closest distance they can get to the wall is 100 m and the initial speed of the heated rocks is 80 m/s. To successfully catapult the rocks over the wall, the minimum angle should be where the maximum height of the trajectory is 16 m, and the maximum angle should be where the range is 100 m. The commander must set up equations of motion to determine the appropriate angle for the catapult.
  • #1
Ravey
5
0
1. A medieval city has the shape of a square and is protected by walls with length 550 m and height 16 m. You are the commander of an attacking army and the closest you can get to the wall is 100 m. Your plan is to set fire to the city by catapulting heated rocks over the wall (with an initial speed of 80 m/s). At what range of angles should you tell your men to set the catapult? (Assume the path of the rocks is perpendicular to the wall. Round the answer to one decimal place. g ≈ 9.8 m/s2)



2. Nada clue other than some kinematics and vectors



3. Tried using kinematics but failed miserably. Help! C'mon it's about medieval stuff! ;)
 
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  • #2
I guess that means the walls are 550m on each side. Could be total length I suppose but that isn't clear. Anyway you have the distance from the wall

(see attachment for picture)

So I guess you aim it high enough so it just clears the the top of the first wall on the way down, and low enough so it arches over the first wall to the foot of the second wall -- if you can. So set up your equations of motion and get cracking. :-)
 

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  • #3
Your minimum angle would be where max height of the trajectory = 16m, because your projectile has to get over the wall. Maximum would be range = 100m to throw the projectile past the wall.
 
  • #4
Ya LCKurtz is right, you don't seem to now where to start so...

Your at 100 m of the first wall and 650 m of the second you now the highest altitude will be half-way 325m and... It's your homework. :-p
 

What is "Multivariable Motion in Space"?

"Multivariable Motion in Space" refers to the study of the movement of objects in three-dimensional space, where multiple variables such as position, velocity, and acceleration are taken into account. This type of motion is commonly seen in the fields of physics, engineering, and astronomy.

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The main components of Multivariable Motion in Space include position, velocity, acceleration, and time. These variables are used to describe the movement of an object in three-dimensional space.

What is the difference between scalar and vector quantities in Multivariable Motion in Space?

Scalar quantities in Multivariable Motion in Space only have magnitude, such as distance and time. Vector quantities have both magnitude and direction, such as velocity and acceleration. In order to fully describe motion in space, both scalar and vector quantities are needed.

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The equations of motion, such as the kinematic equations of motion, are used to mathematically describe the relationship between an object's position, velocity, acceleration, and time. These equations are essential in analyzing and predicting the motion of objects in space.

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