An ostrich runs north in a straight line for 21 meters. She then turns around and runs 25 meters back toward her nest (south) on the same path. What is her displacement?
and what do you think?
To determine the ostrich's displacement, we need to find the straight-line distance from the starting point to the ending point. Displacement is the shortest path between the initial and final positions, regardless of the actual distance covered.
Here's how we can calculate the ostrich's displacement:
1. Draw a straight line representing the initial path of the ostrich for 21 meters towards the north.
2. At the end of this line, draw another straight line representing the subsequent path of the ostrich, which covers 25 meters southward (back toward her nest).
3. Connect the starting point and the ending point of these two lines with a straight line.
The resultant line represents the displacement vector. Its length corresponds to the magnitude of displacement, and its direction points from the starting point to the ending point.
The length of the resultant line can be found using the Pythagorean theorem: c² = a² + b², where c is the length of the resultant line, and a and b are the lengths of the initial and subsequent paths, respectively.
In this case, a = 21 meters and b = 25 meters.
Applying the formula:
c² = 21² + 25²
= 441 + 625
= 1066
Taking the square root of both sides, we find:
c = √1066 = 32.67 meters (rounded to two decimal places)
Therefore, the ostrich's displacement is approximately 32.67 meters, pointing from the starting point to the ending point.