At this point in the story, Beasy has driven his car (2+6+4) = 12 km.
He is parked at the thrift store, (2+4) = 6 km East and 6 km North of his starting point.
As the crow flies, the thrift store is √(6km² + 6km²) in a straight line from the starting point.
That's √(72 km²) , which works out to 8.485 km . When rounded to the nearest whole km, he can phone up his wife and tell her he's "eight kilometers from home can you hear me now ?".
Displacement is a vector, so to answer the question completely, we also need to state its direction.
The angle from home to the thrift store, relative to East, is arctan(6km/6km).
That's 45 degrees.
The full displacement vector is 8.485 km Northeast.
From the question, Beasy drives 2km East and 6 km North. He then drives 4 km East of the first errand. An illustrative diagram is shown in the attachment below.
From the diagram S is the starting starting point, C is coffee shop and T is the thrift store.
The displacement of the car from the starting point is giving by /TS/ in the diagram. To calculate /TS/, consider the right-angled triangle TSQ, /TS/ is the hypotenuse.
From The Pythagorean theorem, in a right-angled triangle, the square of the longest side (hypotenuse) equals sum of the squares of the other two sides.
That is,
/TS/² = /SQ/² + /TQ/²
But /TQ/ = /CP/ = 6km
and /SQ/ = /SP/ + /PQ/
/SP/ = 2 km, /PQ/ = 4 km
∴ /SQ/ = 2 km + 4 km
/SQ/ = 6 km
Hence,
/TS/² = 6² + 6²
/TS/² = 36 + 36
/TS/² = 72
/TS/ = [tex]\sqrt{72}[/tex]
/TS/ = 8.485 km
/TS/ ≅ 8 km ( to the nearest km)
Hence, the displacement of the car from the starting point rounded to the nearest km is 8 km.
Learn more about displacement here: https://brainly.com/question/19232260
