Calculating Distance Between Two Vectors in a Camping Scenario

[Crusaderking1]

Homework Statement

You are camping with two friends, Joe and Karl. Since all three of you like your privacy, you don't pitch your tents close together. Joe's tent is 24.0 m from yours, in the direction 23.0 degrees north of east. Karl's tent is 43.5 m from yours, in the direction 41.0 degrees south of east.

What is the distance between Karl's tent and Joe's tent?

Homework Equations

Karl's tent d_k = 32.83{i) -28.54{j}
Joe's tent d_j = 22.09{i}+ 9.38{j}

The Attempt at a Solution

Karl's tent d_k = 32.83{i) -28.54{j}
Joe's tent d_j = 22.09{i}+ 9.38{j}

d_kj=d_kjx{i}+d_kjy{j}

9.38 + d_kjy=-28.54
22.09{i}+d_kjx=32.83

22.09-32.83= -10.74
9.38+28.54 = 37.92

(10.74)²+(37.92)² and then square root = 39.41m.

Is that right. Thanks!

 

[lewando]

Final answer looks too big. Assuming your location is at the origin, d_j looks fine, but shouldn't d_k have a negative j component?

 

[Crusaderking1]

Final answer looks too big. Assuming your location is at the origin, d_j looks fine, but shouldn't d_k have a negative j component?

Ok, I changed it to 39.41 meters.

 

[lewando]

Much better !

 

[Crusaderking1]

Much better !

thanks!