The instataneous position of an object is specified by its position vector R leading from a fixed origin to the location of the point object. Suppose that a certain object the postion vector is a function of time, given by R=4i+3j-2tk ,where R in meters and t is in seconds. Evaluate dR/dt , what does it represent about the object?
2006-10-13 01:42:54 · 3 answers · asked by Scaryhunter 2 in Education & Reference ➔ Homework Help
Since the position vector is a function of time:
R = 4i + 3j + 2tk
Since the i and j portions of the vector are not expressed as being related to time, they are constants. The derivative of any constant is 0.
Therefore dR/dt = 2k, meaning that the object only moves in k direction as time goes on.
2006-10-13 02:58:41 · answer #1 · answered by ³√carthagebrujah 6 · 0⤊ 0⤋
whilst including vectors, it extremely is sweet to apply genuine advantageous angles and to apply X Y diagrams. east=0 ranges north=ninety ranges west=a hundred and eighty ranges south=270 ranges to characteristic vectors, you ought to transform polar to rectangular coordinates, then upload them. 10 ranges N of E=10 ranges 30 ranges S of E=(-30) ranges from 0 ranges or 330 ranges (genuine). So: a hundred and twenty(cos 10)i+a hundred and twenty(sin 10)j a hundred and fifty(cos 330)i+a hundred and fifty(sin 330)j (by using using genuine angles, you do not ought to subject approximately + and - signs and indicators, by way of fact the calculator will do it for you, once you put in the genuine perspective.) After including the two vectors above, use Pythagorean to discover the magnitude and the arc tan function to discover the perspective. (Remembering tan=sin/cos
2016-10-16 03:49:39 · answer #2 · answered by Anonymous · 0⤊ 0⤋
dR/dt is a derivative. You need to graph the function and find the rate of change at a specific point. (change/length of period), using a tangent line. good luck!
2006-10-13 02:08:29 · answer #3 · answered by BeC 4 · 0⤊ 0⤋