A car is driven east for a distance of 49 km, then north for 28 km, and then in a direction 32° east of north for 27 km. Determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

Question
Asked Feb 11, 2019
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A car is driven east for a distance of 49 km, then north for 28 km, and then in a direction 32° east of north for 27 km. Determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

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Expert Answer

Step 1

The car moves 49km towards east, 28 km towards north and then 27 km towards 32̊ east of north.

 

The expression for the magnitude of the net horizontal displacement of the car is,

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Step 2

Here, dx is the total horizontal displacement of the car, d1 is the magnitude of the first displacement of the car, θ1 is the angle made by the first displacement of the car with east direction, d2 is the magnitude of the second displacement of the car, θ2 is the angle made by the second displacement of the car with east direction, d3 is the magnitude of the third displacement of the car and θ3 is the angle made by the third displacement of the car with east direction.

 

Thus, the magnitude of the net horizontal displacement of the car is,

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Step 3

The expression for the magnitude of the net ...

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