A car travels 20 km west and then 20 km south.What is the magnitude of its displacement vector?
A)0 km
B)20 km
C)28 km
D)40 km

Question

Quizplus · Accepted Answer

The displacement vector is the straight-line distance from the initial point to the final point. We can find the displacement vector by drawing a straight line from the starting point to the ending point. This forms a right-angled triangle with sides of 20 km and 20 km. Using the Pythagorean theorem, we can find the magnitude of the displacement vector:

Magnitude of displacement vector = sqrt((20 km)^2 + (20 km)^2) 
= sqrt(800) 
= 28.28 km (rounded to the nearest hundredth)

Therefore, the correct answer is C, 28 km. Option A is incorrect because the car did move, so the displacement vector cannot be zero. Option B is incorrect because the car moved in two directions and the magnitude of displacement takes into account both directions. Option D is incorrect because adding the two distances together gives the total distance traveled by the car, but does not give us the magnitude of the displacement vector.

A Car Travels 20 Km West and Then 20 Km