A bus travels 6km east and then 8km south. The magnitude of the bus’s resultant displacement is _ km

Hey there! Here's your

10 km

Here's why:

The bus's displacement has two components, a number of km and the direction of the final position from the initial position.

The bus's displacement is the hypotenuse of the triangle, 10 km southeast of the initial position.

But southeast is only a rough estimate of the direction.

The tangent of the angle is 6/8 or .75, so the amount of angle to the east of south is 37 degrees.

South (180 degrees) minus 37 degrees is 143 degrees.

The car’s displacement is more accurately called 10 km in a direction of 143 degrees from the initial point.

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