A boy starts at P and walks 3.0 m due north from P to Q and then 4.0 m due east from Q to R. What is the shortest distance that he must now walk to have an overall displacement of zero?*1 point3.0 m4.0 m7.0 m5.0 m
Question
A boy starts at P and walks 3.0 m due north from P to Q and then 4.0 m due east from Q to R. What is the shortest distance that he must now walk to have an overall displacement of zero?*1 point3.0 m4.0 m7.0 m5.0 m
Solution
The boy started at point P and walked to point R via point Q. To have an overall displacement of zero, he needs to return to his starting point, which is point P.
The shortest distance he can walk to return to point P from point R is along the straight line connecting these two points. This forms a right-angled triangle PQR, where PQ is 3.0 m, QR is 4.0 m, and PR is the hypotenuse.
We can use the Pythagorean theorem to find the length of PR. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, PR² = PQ² + QR² => PR² = (3.0 m)² + (4.0 m)² => PR² = 9.0 m² + 16.0 m² => PR² = 25.0 m² => PR = √25.0 m² => PR = 5.0 m
So, the shortest distance that he must now walk to have an overall displacement of zero is 5.0 m.
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