The Units of a Position Vector in a Hilly Landscape

AI Thread Summary
The discussion centers on the confusion regarding the units of a position vector in a hilly landscape scenario. The position vector is expressed in terms of kilometers per hour and involves trigonometric functions, leading to questions about the differentiation process. Participants clarify that the units of the position vector should be understood as length, not speed, and address the negative sign in the differentiation of the cosine function. The original poster acknowledges their misunderstanding and expresses gratitude for the clarification. Overall, the conversation highlights the importance of understanding both the mathematical concepts and the correct interpretation of units in physics.
amcqueen
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My problem is not so much the mathematics of doing the question, but rather the units.

The question states: "A car travels across a hilly landscape with a position vector given in the x - z plane.

Position Vector = 30 km/hti + 1 km cos (t/(0.1h))k

How can the units for a position vector be given as km/h ?
 
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The units are not km/h, the units are that of km/h*t = Length/time * time = length.
 
ok, i see it now, thanks
 
I'm struggling with the maths side of this question. I've done some searching and came across an answer of v(t) = i30 - k10sin10t and I kind of understand this. I do not understand why the sin is negative though. Could anyone run through the differentiation of this?

Thanks!
 
Caldo120 said:
I do not understand why the sin is negative though. Could anyone run through the differentiation of this?
You're asking where the minus sign comes in when finding d(cosx)/dx? Have you studied calculus?

Try: http://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions"
 
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oh dear. apologies. I was flicking through my table of "INTEGRALS" and wondering why it didn't make sense. Thoroughly embarrassed.

Thank you though for showing me I must pay more attention!
 

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