Kinematics problem - changing coordinates

In summary, the conversation discusses the possibility of solving a question about finding the down slope distance of an arrow by making the x-axis the slope direction. One person suggests trying it out and mentions the use of acceleration on two axes. Another person notes that they didn't consider horizontal acceleration and questions if it is possible to solve the problem by changing the coordinate axes. The conversation also mentions the use of kinematic equations and the use of specific numbers versus general variables in solving the problem.
  • #1
StillAnotherDave
75
8
Homework Statement
Is it possible to solve this problem by changing the coordinate axes?
Relevant Equations
Kinematic equations
Hi folks,

See below for a solved question finding the down slope distance of an arrow. How easy would it be to solve this question by making the x-axis the slope direction?

1586512522048.png
 
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  • #2
StillAnotherDave said:
How easy would it be to solve this question by making the x-axis the slope direction?
One way to find out is to do it ! You'll have acceleration on two axes.
 
  • #3
Aha, yes horizontal acceleration is what I didn't consider.
 
  • #4
StillAnotherDave said:
Homework Statement:: Is it possible to solve this problem by changing the coordinate axes?
Relevant Equations:: Kinematic equations

Hi folks,

See below for a solved question finding the down slope distance of an arrow. How easy would it be to solve this question by making the x-axis the slope direction?

View attachment 260327
It's interesting to see something as advanced as this done with specific numbers, rather than with general variables. It can't be any harder to do it generally.

But, I guess "plug-n-chug" is what's taught these days.
 
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Likes BvU
  • #5
Or is the exercise from an old book :wink: ?
 

Related to Kinematics problem - changing coordinates

1. What is kinematics and how does it relate to changing coordinates?

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. Changing coordinates is a mathematical concept that involves shifting the origin or reference point of a coordinate system. In kinematics, changing coordinates allows us to analyze the motion of an object from different perspectives, making it easier to understand and solve problems.

2. What are the different types of coordinate systems used in kinematics?

The two main types of coordinate systems used in kinematics are Cartesian coordinates and polar coordinates. Cartesian coordinates use x, y, and z axes to describe the position of an object in three-dimensional space. Polar coordinates use a distance from the origin and an angle to describe the position of an object in two-dimensional space.

3. How do you convert between Cartesian and polar coordinates?

To convert from Cartesian coordinates to polar coordinates, you can use the equations r = √(x² + y²) and θ = tan⁻¹(y/x). To convert from polar coordinates to Cartesian coordinates, you can use the equations x = r cos(θ) and y = r sin(θ).

4. How do you solve a kinematics problem involving changing coordinates?

To solve a kinematics problem involving changing coordinates, you first need to identify the given information, such as initial and final positions, velocities, and accelerations. Then, you can use equations of motion, such as s = ut + ½at², to calculate the unknown variables. It is important to keep track of the coordinate system being used and to convert between coordinate systems if necessary.

5. Can you provide an example of a kinematics problem involving changing coordinates?

Sure, here's an example: An object is launched from the origin with an initial velocity of 20 m/s at an angle of 30 degrees above the horizontal. Find the time it takes for the object to reach a height of 10 meters above the ground. To solve this problem, we can use the y-component of the velocity (v₀y = v₀sinθ) to calculate the time it takes for the object to reach a maximum height of 10 meters. Then, we can use the x-component of the velocity (v₀x = v₀cosθ) to calculate the time it takes for the object to travel horizontally from the origin to the point where it reaches a height of 10 meters. Finally, we can add these two times to find the total time it takes for the object to reach a height of 10 meters.

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