a car travelled 15km towards east, 20km towards south and 45km towards the east. represent the movement of the car graphically and determine the total distance travelled by car and displacement of the car
Answers
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Just connect the lines well.
Total distance covered is 15 + 45 + 20 = 80km
To find the total displacement covered, connect the start and end points by a straight line you will get a diagonal intersecting with the vertical line.
Let the the diagonal line cut the vertical line in the parts X km and 20-X km
So the diagonal line can also be divided into two parts, one on the left and one on the right.
You can see that the two triangles formed are similar. Since one the ratio of the sides is 15:45 the ratio pf other corresponding sides must also be the same.
Hence we can say that X is 5km and 20-X is 15km to get the same ratio.
Now apply Pythagoras theorem in each triangle.
Hence the total Displacement (S):
S = (15^2+5^2)^0.5 + (15^2+45^2)^0.5
S = (225 + 25)^0.5 + (225 + 2025)^0.5
S = 250^0.5 + 2250^0.5
S = 63.245 km approximately
Answer:
Graphicall representation would be
___
|
|
|
|
_________
Just connect the lines well.
Total distance covered is 15 + 45 + 20 = 80km
To find the total displacement covered, connect the start and end points by a straight line you will get a diagonal intersecting with the vertical line.
Let the the diagonal line cut the vertical line in the parts X km and 20-X km
So the diagonal line can also be divided into two parts, one on the left and one on the right.
You can see that the two triangles formed are similar. Since one the ratio of the sides is 15:45 the ratio pf other corresponding sides must also be the same.
Hence we can say that X is 5km and 20-X is 15km to get the same ratio.
Now apply Pythagoras theorem in each triangle.
Hence the total Displacement (S):
S = (15^2+5^2)^0.5 + (15^2+45^2)^0.5
S = (225 + 25)^0.5 + (225 + 2025)^0.5
S = 250^0.5 + 2250^0.5
S = 63.245 km approximately