Total Displacement with directions

[tinnguyen123]

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

 

[tiny-tim]

hi tinnguyen123!

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!

30° east of north means 30° from north

(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)

 

[tinnguyen123]

lol omfg >.< thank you.. lame! so its a phi angle..