Two beetles run across flat sand, starting at the same point. beetle 1 runs 0.41 m due east, then 0.72 m at 38o north of due east. beetle 2 also makes two runs; the first is 1.74 m at 48o east of due north. what must be (a) the magnitude and (b) the direction (relative to the east direction in the range of (-180°, 180°)) of its second run if it is to end up at the new location of beetle 1?

a) The magnitud is 0.78m.

b) The direction is .

Explanation:

Beetle 1 runs 0.41m due east, then 0.72m at north of due east.

This means that it's vector position at the end for Beetle 1 is (in vector notation):

⇒

Beetle 2 first run is 1.74m at east of due north, this is:

What's the difference between the final position of Beetle 1 and the position of the Beetle 2 after the first run? This difference will be the vector related to the second run of Beetle 2. This will be:

⇒

a) The magnitud the this second run will be:

.

b) If is the direction of ⇒ ⇒ .

But from components we know the vector points out to the third quadrant (the angle gave of that value because signs canceled each other). The actual direction is

Ф= - 180° = -113.97°.

snell's law

refractve index = sin incidence / sin refraction