Question

A skater glides along a circular path of radius 7.40 m.

1-If he coasts around one half of the circle, find the magnitude of the displacement vector.

2-What distance has the person skated?

3-If the skater coasts only around 73 degrees of the circle, find the magnitude of his displacement vector.

4-What distance has he skated in this case? 5-What is the magnitude of the displacement if he skates all the way around the circle?

Answer 1

Part 1.

When he coasts around one half of the circle, then since displacement is a vector quantity, So

displacement = final position - Initial position = Diameter of circle

displacement = 2*7.40 = 14.80 m

Part 2.

distance traveled = circumference of half circle = pi*r

distance = pi*7.40 = 23.25 m

Part 3.

Suppose Initial position of skater = (7.40, 0) m = (7.40 i + 0 j) m(where center of circular path is at origin and skater starts from x-axis)

final position = 7.40 m at 73 deg CCW from +ve x-axis

final position = (7.40*cos 73 deg i + 7.40*sin 73 deg j) m = (2.1635 i + 7.0767 j) m

Now

displacement = final position - Initial position = (2.1635 i + 7.0767 j) - (7.40 i + 0 j) = (-5.2365 i + 7.0767 j) m

Magnitude of displacement = |d| = sqrt ((-5.2365)^2 + 7.0767^2) = 8.80 m

Part 4.

distance traveled = circumference covered = r*

= angle covered = 73 deg = 73*pi/180 rad

So,

distance traveled = 7.40*73*pi/180 = 9.43 m

Part 5.

displacement = final position - Initial position = 0 m (since he is at the point from where he started)