*Please show work* 1.) A disoriented physics professor drives 3.21 km north, the
ID: 1778109 • Letter: #
Question
*Please show work*
1.) A disoriented physics professor drives 3.21 km north, then 4.80 km west, and then 1.64 km south.
a.) Use components to find the magnitude of the resultant displacement of this professor.
b.) Use components to find the direction of the resultant displacement of this professor.
2.)You are given two vectors. Vector A is 3i + 4j. Vector B is -5i + 7j. If you add both vectors together, what is the magnitude of the resultant vector?
3.) A highway is to be built between two towns, one of which lies 35.0 kilometers North and 22 kilometers East. What is the shortest length in kilometers of a highway that can be built between the two towns?
Explanation / Answer
Given
1)
writing in the vector form
Let N = 0 i + 3.21 km j
E = 4.8 km i + 0 j
S = 0 i - 1.64 km j
now the resultant of the vectors is R = N+E+S
R = Rx i + Ry j
R = (0+4.8+0)i + (3.21+0-1.64) j
R = 4.8 km i+ 1.57 km j
a)
the magnitude is R = sqrt(Rx^2+Ry^2)
R = sqrt(4.8^2+1.57^2) km
R = 5.05 km
b)
the direction is theta = arc tan (Ry/Rx) = arc tan (1.57/4.8) degrees = 18.11 degrees
2.
Vectors A = 3i + 4j. Vector B = -5i + 7j
A+B = (Ax+Bx) i + (Ay+By)j
=(3-5)i +(4+7)
= (-2 i +11j)
A+B = -2i +11j
magnitude is R = sqrt((-2)^2+11^ ) =s unit 11.18
3.
Given vectors are
town 1 is say vector A = 0 i + 35 km j
town 2 is say vector B = 22 km i + 0 j
the resultant of the vectors is the shortest way to connet them
R = A+B = (Ax+Bx) i + (Ay+By)j
R = (0+22) km i + (35+0)km j
the magnitude is
R = sqrt(22^2+35^2) km = 41.34 km
instead of (22+35) = 57 km to connect them .
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