Question

Please help me! 7 points!! I don’t understand

Answer 1

This is adding two vectors, one magnitude 300 direction east, and one magnitude 100 direction 30 degrees northeast.

For the resulting sum we can use the Law of Cosines or just add up the components.  Let's try it both ways.

Components first.   In the east direction we have

300 + 100 cos 30° = 300 + 100(√3/2) = 386.60 miles per hour

In the north direction we have

0 + 100 sin 30° = 100 (1/2) =  50 miles per hour

So a total speed of

sqrt{386.6^2 + 50^2} = 389.82 miles per hour

Answer: 389.82

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OK let's try the Law of Cosines.   We have sides 300 and 100 and included angle 150°.

$c^2 = 300^2 + 100^2 - 2 (300)(100) \cos 150^\circ$

$c=\sqrt{151961.52422} = 389.82 \quad\checkmark$