Need help on Vector stuff

[Moko]

If a rocket is launched from the ground with velocity V m/s at time t seconds: V = 3i + 5j + (10 - t^2)...
Find the velocity of the rocket at t=2.

Would it just be 6 m/s??

[Jenny_2108]

If a rocket is launched from the ground with velocity V m/s at time t seconds: V = 3i + 5j + (10 - t^2)...
Find the velocity of the rocket at t=2.

Would it just be 6 m/s??

what do you mean dot dot dot... ?!? 

[Moko]

that was meant to be a k

[Lasercookie]

So it looks like you're already familiar with representing vectors with the i-j-k notation.

Find the velocity of the rocket at t=2.
Would it just be 6 m/s??

You're saying that the velocity is 6 m/s. Can you see a problem with that statement? There is a difference between speed and velocity. Velocity is a vector and vectors describe both magnitude and direction. Immediately you can see that an answer of "6 m/s" is wrong.

So we have this vector function for velocity. A vector function takes a few variables and outputs a vector.  I find stating it as V(t), rather than just V is a bit clearer.



So all we need to do is substitute t = 2s into our function



And that's our answer. It might seem a bit abstract to state that the velocity of some object is 3i + 5j + 6k, but give it a bit of thought to what that is actually saying and it'll make sense.

[Moko]

This is how I see it: evaluating at t=2 will give us 3i + 5j+6k

Now since K describes the position upwards, and we are looking at a rocket (it goes up), then the velocity should be just the value that determines the velocity travelled in the k/up direction and that will be 6.

Hence the velocity is in fact 6m/s upwards.

[Lasercookie]

Let's consider the consequences of stating that the velocity is

You've neglected to mention the information given by in the direction of the i and j unit vectors.

You're assuming that the rocket only moves up. What if later, a force were to act on the rocket? In that case, if we assumed that the velocity was just , then we'd be ignoring that the velocity vector is actually on a bit of an angle.

Also another somewhat abstract idea is that the direction of velocity, acceleration and displacement can be distinct. You could be moving up, but have a negative velocity at that point in time. You could be moving upwards, but have a velocity that's pointing in more of a south easterly direction. Or in this case we have a vector that points

is the function that describes the rocket's velocity at any time.

If we take the indefinite integral of this, you could come up with a function that describes it's displacement. Or if you differentiate this, you can come up with a function that describes it's acceleration. You might find it handy to plot the various vectors you get for each point in time (take a look at say, t = 0 to t = 5) and see how the various 'properties' of this rocket's motion changes with time. Drawing out things like that for a few scenarios might make it easier for you to visualise the affect velocity can have on an object's motion .

[Moko]

I understand what you are saying, but in this question the vector k denotes the velocity up. If i was say west and j north, for example, then the object will still be travelling up by whatever value in the k direction. What I mean is that although the particle would travel 3 m/s west and 5 m/s north, no matter what it will cover the 6 m/s up. Now since this question is about a rocket that travels upwards, then when they are asking for the velocity at any time, you cant just give them the function at that time, you must give them the velocity of the object relative to the type of object. Since the rocket travels up, then you will state that it is travelling 6m/s up. If the rocket was travelling west, then you will state that it is travelling 3m/s west and so on...

[pi]

If you were looking for a numerical answer, you'd need to look at "speed", which is the magnitude of the velocity vector What laseredd has said is correct, at t=2, you just sub in for V(2).

If the question was asking for the magnitude of the velocity in the upward direction, the answer indeed would be v=6m/s.

[Moko]

Yeah I just checked now it was 6m/s.
Thanks guys