a car travels a distance of 8 km from p to q then moves 6 km at right angle to PQ find its resultants
1.distance
2.displacement
think of a 3-4-5 right triangle.
The displacement is 10
To find the resultant distance and displacement traveled by the car, we can use the Pythagorean theorem and vector addition.
1. Distance:
The distance traveled is the total length covered by the car. In this case, the car travels 8 km from P to Q and then moves 6 km at a right angle. To find the total distance, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the distance traveled is the hypotenuse of a right triangle with sides of 8 km and 6 km. We can use the Pythagorean theorem equation:
Distance^2 = 8^2 + 6^2
Distance^2 = 64 + 36
Distance^2 = 100
Distance = √100
Distance = 10 km
Therefore, the total distance traveled by the car is 10 km.
2. Displacement:
Displacement is a vector quantity that represents the straight-line distance and direction from the starting point to the final position. To find the displacement, we need to consider both the distance and the direction of the car's motion.
In this case, the car moves 8 km from P to Q horizontally and then moves 6 km at a right angle vertically. Therefore, the displacement can be calculated using the Pythagorean theorem, just like we did for distance.
Displacement^2 = 8^2 + 6^2
Displacement^2 = 64 + 36
Displacement^2 = 100
Displacement = √100
Displacement = 10 km
Since displacement is a vector quantity, we also need to consider the direction. In this case, the displacement is the straight-line distance from the starting point P to the final position Q. So, the displacement is 10 km from P to Q, in the direction of Q relative to P.
Therefore, the resultant distance and displacement traveled by the car are both 10 km.