Paramaterization of position and velocity vector

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Homework Help Overview

The problem involves the motion of a stone thrown from a rooftop, described by a position vector in three-dimensional space. The task is to determine the time at which the stone hits the ground, with the position vector given in terms of time.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relevance of maximum height to the problem and whether calculating velocity is necessary. There are attempts to derive the height formula from the position vector and questions about the implications of the k dimension.

Discussion Status

Participants are exploring different aspects of the problem, including the relationship between height and time. Some have suggested using vector calculus methods, while others are focused on the k dimension and its significance in determining when the stone hits the ground. There is no explicit consensus, but several productive lines of inquiry are being pursued.

Contextual Notes

Participants are navigating the constraints of the problem, including the need to avoid overly complex physics concepts while still seeking a solution based on the provided vector equations.

-EquinoX-
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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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What is the question? Are you supposed to calculate the velocity of the stone at time t?
 
I just revised it
 
I don't understand how knowing the maximum height the stone reaches helps. Explain.
 
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
 
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.
 
doesn't this give you that formula?

r(t) = 10ti - 5tj - (6.4 - 4.9t^2)k:
 
Last edited:
-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".
 
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:

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