How can I find the initial velocity of a projectile on an incline?

Click For Summary

Homework Help Overview

The discussion revolves around determining the initial velocity of a projectile launched from a cannon positioned at the bottom of a hill inclined at 9 degrees. The projectile is aimed at an angle of 25 degrees above the incline, and the landing point is 55 meters up the incline. Participants are exploring kinematic equations and the relationships between the components of motion.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the use of kinematic equations to relate the motion of the projectile to its launch angle and time of flight. There are attempts to derive equations for the trajectory and to solve for the initial velocity using various methods, including simultaneous equations and parametric equations.

Discussion Status

Several participants have shared their calculations and results, with some expressing confusion about the relationships between the velocity components and the angles involved. There is ongoing exploration of the correct angles to use in calculations, and some feedback has been provided regarding the interpretation of the incline's effect on the projectile's motion.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information available for solving the problem. There is also a recognition of potential errors in previous calculations and assumptions about angles and components.

Riman643
Messages
62
Reaction score
2
Homework Statement
A very tall hill has a steady incline 9 degrees above the horizontal. A cannon is at the bottom of the hill and aimed an angle 25 degrees above the incline of the hill. After the cannon s fired the ball lands 55 meters up the hill (measured along the incline). Calculate the launch speed of the cannon ball.
Relevant Equations
Basic Kinematic Equations
I have tried for a couple hours now and I just cannot seem to figure out what to do. I am able to to find the the x and y components for acceleration (Xa = 0, Ya = -9.8) and distance (Δx = 54.32, Δy = 8.60) but without any of the other components I am having trouble finding Vo. Any help with pointing me in the right direction would be greatly appreciated.
 
Physics news on Phys.org
Riman643 said:
Problem Statement: A very tall hill has a steady incline 9 degrees above the horizontal. A cannon is at the bottom of the hill and aimed an angle 25 degrees above the incline of the hill. After the cannon s fired the ball lands 55 meters up the hill (measured along the incline). Calculate the launch speed of the cannon ball.
Relevant Equations: Basic Kinematic Equations

I have tried for a couple hours now and I just cannot seem to figure out what to do. I am able to to find the the x and y components for acceleration (Xa = 0, Ya = -9.8) and distance (Δx = 54.32, Δy = 8.60) but without any of the other components I am having trouble finding Vo. Any help with pointing me in the right direction would be greatly appreciated.
You might want to look in both directions and solve 2 simultaneous equations with 2 unknowns.
 
Start with the basic equations of motion for the cannon ball (x and y components of the motion in terms of the launch angle and time). Note that these are parametric equations in terms of t. Then see if you can't render these into a single equation for the trajectory, i.e. y = f(x). The initial launch speed remains an unknown at this point. This trajectory equation intersects the line that represents the hill's surface at a known location...
 
  • Like
Likes   Reactions: Riman643
Ok so after thinking about the feedback I was able to determine that the time = 3.05 seconds. With this I was able to calculate the Initial velocity in all directions. I got the following results:

Vo = 32.98 m/s
Vox = 17.80 m/s
Voy = 17.76 m/s

The problem is that the velocities do no match up using the Pythagorean theorem. I was able to get the time by making Vox = 54.32/t and Voy = 4.9t + (8.6/t) and setting them equal to one another. I guess I'm just confused where I went wrong. Because if I can find Vo at the 9 degree angle I will be able to find it at the 25 degree angle using trigonometry.
 
Riman643 said:
Ok so after thinking about the feedback I was able to determine that the time = 3.05 seconds. With this I was able to calculate the Initial velocity in all directions. I got the following results:

Vo = 32.98 m/s
Vox = 17.80 m/s
Voy = 17.76 m/s

The problem is that the velocities do no match up using the Pythagorean theorem. I was able to get the time by making Vox = 54.32/t and Voy = 4.9t + (8.6/t) and setting them equal to one another. I guess I'm just confused where I went wrong. Because if I can find Vo at the 9 degree angle I will be able to find it at the 25 degree angle using trigonometry.
But Voy and Vox are not equal. They are trig related by vector components at the 25 degree initial angle.
 
Okay so I changed my time equation to 54.32tan(9) = 4.9t^2 + 8.6 and now the Pythagorean theorem works for all the Vo vectors. I got Vo = 2075.07 m/s.

To find Vo at the 25 degree angle I used the Vo I just found as the new x-axis and calculated Vo = 2075.07/cos(25) = 2289.53 m/s.

However this answer seems extremely fast, so I do not think this is correct.
 
Riman643 said:
Okay so I changed my time equation to 54.32tan(9) = 4.9t^2 + 8.6 and now the Pythagorean theorem works for all the Vo vectors. I got Vo = 2075.07 m/s.

To find Vo at the 25 degree angle I used the Vo I just found as the new x-axis and calculated Vo = 2075.07/cos(25) = 2289.53 m/s.

However this answer seems extremely fast, so I do not think this is correct.
Yeah that’s real fast , good observation.

You are getting mixed up on a couple of points. The 9 degree incline has nothing to do with the initial velocity components. It just establishes the x and y coordinates at the landing. It is the 25 degree angle that determines the initial velocity x and y components.

Also, don’t get careless with your equations. The second one is not correct
 
Okay so I realize now that the angle I should be using is 34 degrees because that is where the ball is launched relative the the horizon. With this realization and a reworking of my time equation I got the following equation:

54.32/t = (4.9t + (8.60/t))/tan(34), where t = 2.39 seconds

With t figured out I find Vox = 54.32/2.39 = 22.73

And with Vox I find Vo = 22.73/cos(34) = 27.41

I believe that 27.41 is the final answer. But I could be wrong yet again.
 
Last edited:
Looks good now! I'd round it off to 27 m/s
 
  • Like
Likes   Reactions: Riman643
  • #10
Awesome. Thank you so much!
 

Similar threads

Finding the acceleration of a block on an inclined plane with friction
  • · Replies 2 ·
Replies
2
Views
694
Projectile Motion: initial velocity problem
  • · Replies 1 ·
Replies
1
Views
2K
Find the range of an object coming off an inclined plane
  • · Replies 1 ·
Replies
1
Views
2K
How do you find the initial velocity of a projectile given angle/distance?
  • · Replies 3 ·
Replies
3
Views
2K
How to find the max height a projectile can reach on a hillside
  • · Replies 12 ·
Replies
12
Views
3K
seeking help finding the initial velocity of a type 3 projectile
  • · Replies 5 ·
Replies
5
Views
1K
Projectile Motion: time it takes for projectile to hit truck
  • · Replies 15 ·
Replies
15
Views
3K
What is the total distance traveled by a bullet fragment after an explosion?
  • · Replies 13 ·
Replies
13
Views
2K
Projectile Motion - Range of projectile
  • · Replies 5 ·
Replies
5
Views
2K
What is the Launch Angle of a Projectile at Half Its Maximum Height?
  • · Replies 3 ·
Replies
3
Views
2K