An automobile travels 30 km due east on a level road . It then turns due north at an intersection and travels 40km before stopping. What is the the resultant displacement of the car?

d=sqrt(s₁²+s₂²) =sqrt(900+1600)=50 km

To find the resultant displacement of the car, we need to calculate the total distance traveled in the north and east directions separately, and then combine them to find the overall displacement.

Step 1: Calculate the distance traveled east.
The car travels 30 km due east.

Step 2: Calculate the distance traveled north.
The car then turns due north and travels 40 km.

Step 3: Combine the distances traveled in the east and north directions to find the resultant displacement.
We can use the Pythagorean theorem to find the resultant displacement. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (resultant displacement) is equal to the sum of the squares of the other two sides (distances traveled east and north).

Let's calculate it:
Distance traveled east (E) = 30 km
Distance traveled north (N) = 40 km

Resultant displacement (D) = √(E^2 + N^2)
= √(30^2 + 40^2)
= √(900 + 1600)
= √2500
= 50 km

Therefore, the resultant displacement of the car is 50 km.