question_answer

A room has dimensions 3mx4mx5m. A fly starting at one corner ends up at the diametrically opposite comer, (a) What is the magnitude of its displacement? (b) If the fly does not fly but walks, what is the length of the shortest path it can take?

Answer:

                (a) If the starting point of fly which is one comer of room is taken as origin of coordinates, then the coordinates of diametrically opposite comer of room are (3, 4, 5). So displacement is \[\overset{\to }{\mathop{r}}\,=3\hat{i}+4\hat{j}+5\hat{k}\] and \[r=\sqrt{{{3}^{2}}+{{4}^{2}}+{{5}^{2}}}=\sqrt{50}\approx 7m\] (b) When the fly walks, then shortest distance travelled is \[=3+\sqrt{{{4}^{2}}+{{5}^{2}}}=3+\sqrt{41}=9.4m\]