physics help: a car travels 215 km w and then 85 km south west : find the magnitude and direction?

Answer 1

You could draw it, then measure the resultant.
I can't do that here so :
85 km SW is 85/sqrt(2) km S and the same distance W . Total distance W is therefore 215+85/sqrt(2) and S is 85/sqrt(2)

magnitude will be the above all squared and summed then find root
sqrt(215^2+ 2*85^2/2 + 2*215*85/sqrt(2) )

which is about 282 km. West by Southwest

(in the above: sqrt() means take the square root of ; * is multiply and ^ is raised to the power of ; / is divide)

Answer 2

(1) 215Km Distance: 215Km West and 0Km South.

(2) 85Km Distance:
West Distance is Cos.45° = Ady / Hyp.
West Distance = Hyp. Cos.45°
West Distance = (85Km)(0∙7071...)
West Distance = 60∙104... Km.

South Distance is Sin.45° = Opp. / Hyp.
South Distance = Hyp. Cos.45°
South Distance = (85Km)(0∙7071...)
South Distance = 60∙104... Km.


Total West Distance = West (1) + West (2).
Total West Distance = 215Km + 60∙104... Km.
Total West Distance = 275∙104... Km.

Total South Distance = South (1) + South (2).
Total South Distance = 0Km + 60∙104... Km.
Total South Distance = 60∙104... Km.

Magnitude = √ [(West Distance) ² + (South Distance) ²]
Magnitude = √ [(275∙104... Km.) ² + (60∙104... Km.) ²]
Magnitude = √ [(75682∙25285) + (3612∙5) ]
Magnitude = √(79294∙75285)
Magnitude = ± 281∙5932401.. Km.

For Angle Θ is: tan^ -1 (Opp./Ady.)
For Angle Θ = tan^ -1 (60∙104... Km../275∙104... Km.)
For Angle Θ = tan^ -1 (60∙104... Km../275∙104... Km.)
For Angle Θ = tan^ -1 ( 0∙218 477 592 )
For Angle Θ = 12∙3241914..° South West.

Answer:
Magnitude ≈ 281∙59 Km. @ an angle of ≈12∙32° South West.

Answer 3

right about .............................. there!