Awildlife researcher is tracking a flock of geese. the geese fly 4.0km due west, then turn toward the north by 40 degrees and fly another 3.5km.

part a: how far west are they of their initial position?
part b: what is the magnitude of their displacement?

a.6.68 km

b.7.01 km

Explanation:

The gees fly due to west=4.0 km

Geese fly another distance due to north=3.5 km

a.We have to find the west distance from their initial position

From below diagram

The x-component of the total distance that geese flies which is the west distance from the initial position

B. The vertical component of total distance that gees flies from initial position

Magnitude of displacement ,D=

Substitute the values then we get

Magnitude of their displacement,D=

Magnitude of their displacement,D=7.01 km

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

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