a car travels due east on the level road for 3km it then turns due north at the intersection and travels 4km before stopping the magnitude of resultant displacement of car
X = 3 km
Y = 4 km
D = sqrt(X^2+Y^2)
5 km
To find the magnitude of the resultant displacement of the car, we can use the Pythagorean theorem.
Let's consider the east direction as the positive x-axis and the north direction as the positive y-axis.
The car travels 3 km due east, so its displacement in the x-direction is +3 km.
Then, the car turns and travels 4 km due north, so its displacement in the y-direction is +4 km.
To find the resultant displacement, we can use the Pythagorean theorem:
Resultant displacement = √(displacement in x-direction^2 + displacement in y-direction^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5 km
Therefore, the magnitude of the resultant displacement of the car is 5 km.
To find the magnitude of the resultant displacement of the car, we can use the Pythagorean theorem.
Step 1: Determine the eastward displacement (horizontal component) from the starting point to the intersection. Since the car travels due east for 3km, the eastward displacement is 3km.
Step 2: Determine the northward displacement (vertical component) from the intersection to the stopping point. Since the car turns due north and travels 4km, the northward displacement is 4km.
Step 3: Use the Pythagorean theorem to calculate the magnitude of the resultant displacement. The Pythagorean theorem states that the square of the hypotenuse (resultant) is equal to the sum of the squares of the other two sides. In this case, the resultant displacement is the hypotenuse.
Using the formula c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the other two sides, we can substitute the values:
resultant^2 = eastward displacement^2 + northward displacement^2
resultant^2 = 3^2 + 4^2
resultant^2 = 9 + 16
resultant^2 = 25
Step 4: Take the square root of both sides to find the magnitude of the resultant displacement:
resultant = sqrt(25)
resultant = 5 km
Therefore, the magnitude of the resultant displacement of the car is 5 km.