Paramaterization of position and velocity vector

In summary, the stone is thrown from a rooftop and its position at time t is given by r(t) = 10ti - 5tj - (6.4 - 4.9t^2)k.
  • #1
-EquinoX-
564
1

Homework Statement


A stone is thrown from a rooftop at time t = 0 seconds. Its position
at time t is given by
r(t) = 10ti - 5tj - (6.4 - 4.9t^2)k:
The origin is at the base of the building, which is standing on at ground. Distance is measured in meters. The vector i points east, and
k points up.

At what time does the stone hits the ground?

Homework Equations


The Attempt at a Solution



I am pretty sure that I need to find the height when the stone reaches the top.. am I right?
 
Last edited:
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  • #2
What is the question? Are you supposed to calculate the velocity of the stone at time t?
 
  • #3
I just revised it
 
  • #4
I don't understand how knowing the maximum height the stone reaches helps. Explain.
 
  • #5
if I know the height of the stone, i.e when the velocity is 0 then I can calculate the time it takes when it hits the ground using h = vo +1/2at^2.. but now it becomes a physics problem.. and I don't want to take it that far.. I should solve this using some vector calculus methods... so any suggestions are appreciated
 
  • #6
Ah, I understand now. Anyways, let me ask you this: Can you give me a formula for the height of the particle at time t.
 
  • #7
doesn't this give you that formula?

r(t) = 10ti - 5tj - (6.4 - 4.9t^2)k:
 
Last edited:
  • #8
-EquinoX- said:
doesn't this give you that formula?

r(t) = 10ti = 5tj - (6.4 + 4.9t^2)k:

You do realize there is a typo in there right? Anyways, r(t) is the position of the particle in 3D space. There is only one dimension we care about (which one?). And yes, r(t) "gives you that formula".
 
  • #9
the k dimension ,right?
 
  • #10
Correct. Now what is the formula for the height at time t?
 
  • #11
(6.4 - 4.9t^2) right? so at t = 0 the height is 6.4... so where are we going on next?
 
  • #12
Yes. So now that you know the height at time t, when does the stone hit the ground?
 
  • #13
e(ho0n3 said:
Yes. So now that you know the height at time t, when does the stone hit the ground?
the stone hits the ground at height 0. I think I got it now... thanks :D
 
Last edited:

1. What is paramaterization of position and velocity vector?

Paramaterization of position and velocity vector is a mathematical process used to describe the position and velocity of an object in motion. It involves breaking down the position and velocity vectors into separate components, such as x, y, and z coordinates, to better understand the motion of the object.

2. Why is paramaterization of position and velocity vector important in science?

Paramaterization of position and velocity vector is important in science because it allows us to accurately describe the motion of objects and make predictions about their future movements. It is also essential in mathematical models used to study various physical phenomena.

3. How is paramaterization of position and velocity vector used in real-world applications?

Paramaterization of position and velocity vector is used in various real-world applications, such as in physics, engineering, and astronomy. It is used to track the motion of objects, predict their future movements, and design systems that rely on precise positioning and velocity control.

4. What are some common methods of paramaterization of position and velocity vector?

Some common methods of paramaterization of position and velocity vector include Cartesian coordinates, polar coordinates, and spherical coordinates. These methods involve different ways of breaking down the position and velocity vectors into separate components.

5. How does paramaterization of position and velocity vector relate to calculus?

Paramaterization of position and velocity vector is closely related to calculus, specifically in the study of derivatives and integrals. Calculus is used to analyze the changing position and velocity of an object over time, which is essential in paramaterization of position and velocity vector. It also helps us to understand the relationship between position, velocity, and acceleration.

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