1. Let\'s assume that an ant decides to start from the point (2, 4) in the (x,y)
ID: 1309174 • Letter: 1
Question
1. Let's assume that an ant decides to start from the point (2, 4) in the (x,y) plane. It decides then to move in straight segments as follows:
* 4 units to the right
* then 3 units up ( +y direction)
* then 1 unit to the left
* and finally 6 units at an angle (- 60) degrees with respect to the (+x axis)
Calculate the magnitude of the total displacement and the total distance traveled
2. You walk from the middle row of "horses" of a Merry-Go-Round to the outer row. What happens to your rotational speed? Your tangential speed?
Explanation / Answer
1. The initial position is (2,4)
x_0 = 2i + 4j
the subsiquen movements ,
4 units to the right = + 4i
* then 3 units up ( +y direction) = 3 j
* then 1 unit to the left = - 1i
* and finally 6 units at an angle (- 60) degrees with respect to the (+x axis) = 6 { (3i - 4j ) /5 } = 3.6 i - 4.8j
because the unit vector along it is (3i - 4j ) /5
so , the displacement is = 4i + 3j - i + 3.6i - 4.8j = 6.6i - 1.8 j
magnitude = 6.84 units
Total distance travelled = 4 + 3 +1 + 6 = 14 units
2. As we move to the further rows,
the rotational speed remains the same
the tangential veocity increases as the distance from the center increases
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.