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One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 2.97 km. They start at the west side of the lake and head due south to begin with. (a) What is the distance they travel? (b) What is the magnitude of the couple’s displacement? (c) What is the direction (relative to due east) of the couple’s displacement?

Sagot :

The distance they travel is 4.85 km. the magnitude of the couple’s displacement is 1.456 km. The displacement vector is 315 degrees counterclockwise in relation to the east.

The total distance traveled is the overall distance traveled during the entire excursion. However, the displacement is the net distance traveled between the starting location and the final position. Displacement cannot exceed distance in any way. An element of a vector is the displacement. It is a scalar quantity, the distance.

The couple circles a circular lake on foot about 3/4 of the way.

The circle has a radius of r = 1.03 km, or 1030 meters.

The couple's journey begins at point A and ends at point D by taking the path ABCD.

The journey's distance is calculated as follows:

d = 0.75*2*3.14*1.03*d

=4.85 km

The net distance between points A and D is the displacement's magnitude. |d| = |AD|=|r2+r2

= 21.03/2

=1.456 km

The displacement vector is 315 degrees counterclockwise in relation to the east.

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