A car travels 2.21 km in the x-direction, then turns left 65.5◦ to the original direction and travels an additional distance of 1.78 km. Calculate the x component of the car’s net displacement. Let: d1=2.21 km, θ = 65.5◦ d2 = 1.78 km . Answer in units of km.  

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The initial displacement of the car on the x-axis is 

2.21 km (East).

The car then turns left bearing at an angle of 65.5 degrees from East, to now travel NE.

It then travels 1.78 km in that new direction.

To find the negative displacement on the x-axis following...

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The initial displacement of the car on the x-axis is 

2.21 km (East).

The car then turns left bearing at an angle of 65.5 degrees from East, to now travel NE.

It then travels 1.78 km in that new direction.

To find the negative displacement on the x-axis following this change of course, we can use the trigonometric relation

cos (theta) = A/H

where x is the angle between the adjacent side A of the triangle and the hypotenuse H of the triangle.

We already have theta = 65.5 degrees and H = 1.78 km

Solving for the length A, we obtain the positive displacement on the x-axis.

A = cos (65.5) x H = 0.41469 x 1.78 = 0.7382 km

Adding this from the initial displacement of the car on the x-axis we find that the final resulting net displacement on the x-axis is.

2.21 km + 0.7382 km = 2.9482 km

The net displacement of the car on the x-axis is 2.9482 km.

 

 

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