The figure below gives the path of a squirrel moving about on level ground, from

Question

The figure below gives the path of a squirrel moving about on level ground, from point A(at time t = 0), to point B(at t = 4.20 min), C(at t = 8.40 min), and finally D(at t = 12.6 min). velocities of the squirrel from point ?A to each of the other three points. (a) Of the three average velocities, which has the least magnitude? What is this average velocity in magnitude-angle notation? m/s, degree counterclockwise from the +x-axis (b) Which has the greatest magnitude? What is this average velocity in magnitude-angle notation? m/s, degree counterclockwise from the +x-axis

Explanation / Answer

coordinates of the points are:

A: (15,-15)

B: (30,-45)

C: (20,-15)

D: (45,45)

displacement from A to B=sqrt((30-15)^2+(-15+45)^2)=33.541 m

then average velocity=total displacement/total time taken=33.541/4.2 m/min

=7.986 m/min

displacement from A to C=sqrt((20-15)^2+(-15+15)^2)=5 m

then average velocity=total displacement/total time taken=5/8.4 =0.59524 m/min

displacement from A to D=sqrt((45-15)^2+(-15-45)^2)=67.082 m

then average velocity=total displacement/total time taken=67.082/12.6=5.324 m/min

so average velocity from A to C has least magnitude.

magnitude=0.59524 m/min=0.00992 m/s

direction from A to C is along +ve x axis

so angle will be 0 degrees

part b:

greatest magntitude is from A to B.

magnitude=7.986 m/min=0.1331 m/s

direction is from A to B.

unit vector from A to B=(30-15,-45+15)/33.541

=(0.44721,-0.89443)

angle with +ve x axis=arctan(-0.89443/0.44721)=-63.435 degrees

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