A car travel a distance of 8 km frome P to Q then moves 6 km at right angles to PQ .Find its travel distance and displacement

Solution

distance=sqrt(8^2+4^2)

displacement...you will have to measure the angle relative to PQ.

d = 8 + 6 = 14 km = Travel distance.

D^2 = 8^2 + 6^2 = 100,
D = 10 km = Displacement.

To find the total travel distance of the car, we need to add up the distances it traveled in each leg of the journey.

1. The car traveled 8 km from P to Q. This is a straight line distance, so the travel distance for this leg is 8 km.

2. The car then moved 6 km at right angles to PQ. This means it went from point Q to a new point R, forming a right-angled triangle with PQ as the horizontal leg and PR as the vertical leg. The total distance traveled in this leg can be found using the Pythagorean theorem.

a. The horizontal leg PQ has a length of 8 km.
b. The vertical leg PR has a length of 6 km.

Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of the hypotenuse QR as follows:

c^2 = 8^2 + 6^2
= 64 + 36
= 100

Taking the square root of both sides, we find that c = 10. Therefore, the distance traveled in this leg is 10 km.

Now, to find the total travel distance, we simply add up the distances from each leg:

Travel distance = 8 km + 10 km
= 18 km

So, the total travel distance of the car is 18 km.

To find the displacement of the car, we need to consider the straight-line distance and direction from the initial point to the final point.

1. The car traveled 8 km from P to Q. This is a straight line distance.

2. The car then moved 6 km at right angles to PQ to reach the point R.

To find the displacement, we can draw a vector diagram. Starting from point P, draw an arrow to represent the straight-line distance and direction to the final point R.

The displacement is the length of this arrow. By measuring the length of this arrow on the diagram or using the Pythagorean theorem, we find that the displacement is 10 km.

Therefore, the displacement of the car is 10 km.