Bob walks 370 m south, then jogs 410 m southwest, then walks 370 m in a direction 28 degrees east of north.

Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a distance.

Find the direction of the displacement that will return Bob to his starting point by the most direct route.

Question

Bob walks 370 m south, then jogs 410 m southwest, then walks 370 m in a direction 28 degrees east of north. 

Use either trigonometry or components to find the displacement that will return Bob to his starting point by the most direct route. Give your answer as a distance.

Find the direction of the displacement that will return Bob to his starting point by the most direct route.

anonymous · Answer

ok i figured this out. you have to write out all the x an y components. it helps to draw a picture soo....|dw:1328766942259:dw|

ok so our x component for the first part is 0 because it goes straight down. then y is -370.

second part takes some trig. and you have to darw your triangle and use 45 degree as your angle. so doing 410cos(45) and 410sin(45) you get 290, both negative x and y components. then the third line is 28 degrees. so using 370sin(28) and 370cos(28) you get your x component= 173.7 and y= 326.7 then add em all up and it will give you

326.7-370-290= -333.3 for the y direction
173.7- 290 = -116.3 for the x direction. 

so then you have to find your way back to origin. which should be equal to 0. so iff you go 333.3m in the positive up direction and 116.3m east you will be back at origin. so do $$\sqrt{116.3^{2} + 333.3^{2}}$$
and you will have the shortest distance to get back to origin. 

then to find at what angle that is you do $$\tan^{-1} (333.3/116.3)$$ and bam your done. lol

anonymous · Answer

can i give myself a medal for this one lol

king · Answer

rocket science is cake can u pls help me?

anonymous · Answer

help you with what king?