Total Displacement with directions

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The discussion focuses on calculating the total displacement of a car driven in multiple directions. The car travels 48 km east, 26 km north, and then 28 km at an angle of 30° east of north. An initial attempt to calculate the final position using Cartesian coordinates led to incorrect displacement and direction results. Clarification was provided that 30° east of north should be interpreted as 30° from the north axis, which corrected the approach to solving the problem. The conversation emphasizes the importance of accurately understanding vector angles in displacement calculations.
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Homework Statement



A car is driven east for a distance of 48 km, then north for 26 km, and then in a direction 30° east of north for 28 km. Draw the vector diagram and determine the total displacement of the car from its starting point and its direction.


Homework Equations


im not sure.. if i tackle this problem right...
x=rcos
y=rsin

arctan(y/x)= teta


The Attempt at a Solution




I try to find the displacement from (48,26) then add to the (28cos30),(28sin30) which give the final destination point in Cartesian Coordinate.. then i use the distance formula.. but it keep giving me a different answer..

so i got (48+28cos30),(26+28sin30)

then sqrt((48+28cos30)^{2}+(26+28sin30)^{2}) = displacement.. i keep getting 82.5 but the answer is 79.8

and then i use the coordinate to find the dirrection.. but my calc keep giving me 29 degree.. answer is 39
 
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hi tinnguyen123! :smile:
tinnguyen123 said:
A car is driven east for a distance of 48 km, then north for 26 km, and then in a direction 30° east of north for 28 km.
…
so i got (48+28cos30),(26+28sin30)

oops! :redface:

30° east of north means 30° from north :wink:

(so 0° east of north is north, and 90° east of north is east)

(and 90° north of east is north, and 0° north of east is east)
 
lol omfg >.< thank you.. lame! so its a phi angle..
 

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