Cannon ball fired at castle - kinematics

In summary, the problem involves a cannon firing a 10.0kg cannon ball at an initial speed of 100m/s and an angle of 20 degrees above the ground. The goal is to determine the distance above a castle wall, located 500m away, where the cannon ball will pass. The solution involves separating the horizontal and vertical components of motion and using the equation Δx = Vit + 1/2at^2 to calculate the time it takes for the cannon ball to reach the wall. This time is then used in the equation y = (Vi)y*t + 1/2at^2 to calculate the vertical displacement at the wall's location. This value is then subtracted from the height of the
  • #1
yaser1989
6
0

Homework Statement


A cannon fires a 10.0kg cannon ball 1.0m above the ground and at 20o to the horizontal with an initial speed of 100m/s. A castle 500m away has a wall 24.3m high. At what distance above the castle wall does the cannon ball pass?


Homework Equations


Δx = Vit + 1/2at2
It's the only one I can think of that applies.

The Attempt at a Solution


I thought of getting time it takes to get to the wall then using that to calculate displacement above the wall but I got the wrong answer. The only thing I don't know is how to include the mass (10.0kg) in my calculations.
 
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  • #2


Anyone?
 
  • #3


You want to separate the horizontal and vertical component of motion in this problem, which means that you separate the horizontal and vertical component of initial velocity and the horizontal and vertical motion equations. You already listed one motion equation, there should be another one for another direction. It's convenient if you let x be the horizontal component and y be the vertical component.
 
  • #4


I got it.

I rearranged Δx = Vit + 1/2at2 for time:

t = Δx / Vi --> since acc'n in the x direction is 0, 1/2at2 = 0.

So then, t = 500/ 100cosΘ where Θ = 20o
= 5.321.

Then I used y = (Vi )yt + 1/2at2
= (100sinΘ)(5.321) + 1/2(-9.81)(5.3212 )
= 43.11

Subtracted that from the height of the wall - the height of the cannon:

43.11 - 23.3 = 19.81

Thanks for the help !
 

FAQ: Cannon ball fired at castle - kinematics

1. How does the initial velocity of the cannon ball affect its trajectory?

The initial velocity of the cannon ball determines the speed and direction at which the ball will travel. A higher initial velocity will result in a longer and flatter trajectory, while a lower initial velocity will result in a shorter and steeper trajectory.

2. What is the role of gravity in the motion of the cannon ball?

Gravity is the force that pulls the cannon ball towards the ground, causing it to follow a parabolic path. The strength of gravity has a significant impact on the trajectory of the cannon ball.

3. How does the angle of the cannon affect the distance the ball travels?

The angle of the cannon determines the vertical and horizontal components of the initial velocity. A higher angle will result in a greater vertical component, causing the ball to travel higher but not as far horizontally. A lower angle will result in a longer horizontal distance but a lower peak height.

4. How does air resistance affect the motion of the cannon ball?

Air resistance, also known as drag, will act in the opposite direction of the cannon ball's motion, slowing it down and affecting its trajectory. The impact of air resistance will increase as the velocity of the ball increases.

5. How does the mass of the cannon ball affect its motion?

The mass of the cannon ball has a direct impact on its motion, specifically in regards to its acceleration. A heavier cannon ball will require a larger force to accelerate it to a certain speed, while a lighter cannon ball will require less force. However, once the ball is in motion, its mass will not affect its trajectory.

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