Solve King Arthur's Rock Launching Problem

• Sylis
In summary, the knights of King Arthur's castle use a catapult to launch a rock from 12 m above the moat at a velocity of 25m/s and an angle of 30° above the horizontal. By breaking the velocity into horizontal and vertical components, the problem can be solved in pieces. Using the equation Vf2=Vi2 +2aΔx, the maximum height of the rock can be determined. Then, using the fixed flight time, the horizontal distance can be calculated using the horizontal velocity component.

Homework Statement

i
King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 12 m above the moat. The rock is launched at 25m/s and an angle of 30° above the horizontal. How far from the castle wall does the launched rock hit the ground?

Homework Equations

ti=0, xi=0, vi=25, vf=0, a=-9.8
Vf2=Vi2 +2aΔx

The Attempt at a Solution

So I have a picture drawn of a horizontal line representing the ground/moat, and at one end a vertical line which extends 12m to signify the wall, and then another horizontal line signifying the "above the horizontal" part of the problem, and then a line at a negative slop that is at a 30 degree angle which also connects with the wall/horizontal. I believe I'm visualizing this correctly.

I get that horizontal velocity would be 25cos30. I'm just not quite sure what to do with that information. I sat here and thought about it for a bit and figured that if I used ti=0, xi=0, vi=25, vf=0, a=-9.8, I could use Vf2=Vi2 +2aΔx to find the max height of the rock, and solve it in pieces that way, but that doesn't seem like the best use of the information I'm given, and also sort of defeats the purpose of using angles which is part of the lesson. Any thoughts?

Solving it in pieces is actually a great way to work these problems. You seem to be on the right track--maybe the angles lesson is only testing your ablility to properly decompose the velocity, and use each piece appropriately. Treat projectiles as one part vertical motion, and one part horizontal independently.

Once you find your maximum height (and note, your ##v_i≠25## here for finding that out->work out the vertical projection for this like you did the horizontal), think about using that information to find out how long the projectile stays in the air. From there, you should be able to work out the distance using the horizontal velocity you already discovered.

One thing you know is that the flight time is fixed. Whatever flight time results from solving the vertical equations can be used in the horizontal equations.

1. What is King Arthur's Rock Launching Problem?

King Arthur's Rock Launching Problem is a theoretical problem that involves calculating the minimum amount of energy required to launch a rock from a slingshot to hit a target at a certain distance. It is based on the legend of King Arthur and the Knights of the Round Table, where Arthur's knights must launch a rock to hit a target in order to prove their strength and bravery.

2. Why is this problem important?

This problem is important because it demonstrates the principles of physics and mathematical calculations in a real-world scenario. It also challenges scientists to find the most efficient and accurate solution, which can have practical applications in fields such as engineering and projectile motion.

3. What are the main factors to consider in solving this problem?

The main factors to consider in solving King Arthur's Rock Launching Problem include the distance to the target, the weight and size of the rock, the angle and velocity of the launch, and the force of gravity. Other factors, such as air resistance and wind speed, may also need to be taken into account for a more precise solution.

4. How can this problem be solved?

There are several ways to solve King Arthur's Rock Launching Problem. One method is to use the principles of projectile motion and vector analysis to calculate the necessary angle and velocity of the launch. Another approach is to use mathematical formulas and equations, such as the energy conservation equation and the law of cosines, to determine the minimum energy required for the rock to hit the target.

5. Are there any real-world applications of this problem?

Yes, there are several real-world applications of King Arthur's Rock Launching Problem. For example, it can be used to design more efficient slingshots or catapults for launching projectiles. It can also be applied in the field of ballistics to calculate the trajectory of missiles or artillery shells. Additionally, this problem can be used in sports and games that involve throwing or launching objects, such as javelin throwing or archery.