Paramaterization of position and velocity vector

[-EquinoX-]

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?

 

[e(ho0n3]

What is the question? Are you supposed to calculate the velocity of the stone at time t?

 

[-EquinoX-]

I just revised it

 

[e(ho0n3]

I don't understand how knowing the maximum height the stone reaches helps. Explain.

 

[-EquinoX-]

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

 

[e(ho0n3]

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.

 

[-EquinoX-]

doesn't this give you that formula?

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

 

[e(ho0n3]

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".

 

[-EquinoX-]

the k dimension ,right?

 

[e(ho0n3]

Correct. Now what is the formula for the height at time t?

 

[-EquinoX-]

(6.4 - 4.9t^2) right? so at t = 0 the height is 6.4... so where are we going on next?

 

[e(ho0n3]

Yes. So now that you know the height at time t, when does the stone hit the ground?

 

[-EquinoX-]

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