Tangent line to a particles path at a specific time?

In summary, to find the orientation of a line that is tangent to the particle's path at t = 2.10 s (from the +x axis), you first need to find the position, velocity, and acceleration of the particle at that time using the given equations. Then, you can use the inverse tan function to find the angle between the velocity vector and the x-axis. However, in this case, the velocity vector lies in the fourth quadrant, so you need to add 360 degrees to the calculated angle to get the final orientation of 272 degrees from the +x axis in an anticlockwise direction.
  • #1
badtwistoffate
81
0
how do you find orientation of a line that is tangent to the particle's path at t = 2.10 s?(from the +x axis)
before this i found the position r of a particle moving in an xy plane is given by r = (1.00t3 - 8.00t) i + (7.00 - 4.00t4) j.
So I found r,v,a, for t=2.10s (all in m)
r=-7.54 i +-70.8 j
v=5.23 i + -148 j
a=12.6 i + -212 j
i first tried using v's i and j to make a triangle and find the angle from that by inverse tan (-148/5.23) and got -87degress or -212 but that was wrong...
any help?
 
Physics news on Phys.org
  • #2
i got 272 degree from the + x-axis in anticlockwise direction.
 
  • #3
how did u get that?
did you just do the inverse tan and adding to 360? does that make sense?
 
  • #4
your v lies in the fourth quadrant.
 

1. What is a tangent line to a particle's path at a specific time?

A tangent line to a particle's path at a specific time is a line that touches the particle's path at that time and has the same slope as the particle's path at that point.

2. Why is the tangent line to a particle's path important?

The tangent line to a particle's path is important because it helps us understand the direction and speed of the particle's motion at a specific time. It also allows us to make predictions about the particle's future path.

3. How is the tangent line to a particle's path calculated?

The tangent line to a particle's path is calculated by finding the derivative of the particle's position function at the specific time. This derivative represents the instantaneous rate of change of the particle's position at that time, which is equal to the slope of the tangent line.

4. Can the tangent line to a particle's path change over time?

Yes, the tangent line to a particle's path can change over time as the particle's motion changes. This is because the particle's position function and therefore its derivative, which determines the slope of the tangent line, can change over time.

5. How can the tangent line to a particle's path be used in real-world applications?

The tangent line to a particle's path can be used in various real-world applications, such as motion analysis in physics and engineering, predicting the path of projectiles, and modeling the behavior of moving objects in fields like robotics and computer graphics.

Similar threads

  • Introductory Physics Homework Help
Replies
14
Views
824
  • Introductory Physics Homework Help
Replies
2
Views
972
  • Introductory Physics Homework Help
Replies
3
Views
695
  • Introductory Physics Homework Help
Replies
16
Views
666
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
568
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
4K
Back
Top