Final answer:
The correct option for the ratio of the total distance traveled to the magnitude of displacement for a particle moving first eastward then northward is (3) 7/5, calculated using the Pythagorean theorem.
Step-by-step explanation:
The student is asking about the relationship between distance traveled and magnitude of displacement for a particle that moves in two perpendicular directions: east and north.
When the particle travels 3m towards East and then 4m towards North, the total distance traveled is the sum of both movements, which is 3m + 4m = 7m. To find the magnitude of displacement, which is the straight-line distance from the starting point to the final position, we can apply the Pythagorean theorem to these perpendicular vectors.
The magnitude of displacement is the hypotenuse of the right triangle formed by the eastward and northward movements, which calculates to √(3^2 + 4^2) = √(9 + 16) = √25 = 5m. Therefore, the ratio of distance traveled to magnitude of displacement is 7/5.
In conclusion, the correct option for the ratio of distance traveled and magnitude of displacement is (3) 7/5.