CJ10 1.P052 Two north of west, and the second team as 22 km away, 36° east of no
ID: 1881214 • Letter: C
Question
CJ10 1.P052 Two north of west, and the second team as 22 km away, 36° east of north. When the following? I field teams are working in a remote area. A global positioning s tracker at their base camp shows the location of the first team as 32 km away, 13 the first team uses its GPS to check the position of the second team, what does the GPS give for (a) the second team's distance from the first team 45.37 km (b) the second team's direction from the first team, measured relative to due east 28.6 Section 1.8 CJ10 1 P055 Vector A has a m give aExplanation / Answer
let East be +x axis
let r1 = 32 km, r2 = 22 km
r1x = -32*cos(13) = -31.2 km
r1y = 32*sin(13) = 7.20 km
r2x = 22*sin(36) = 12.9 km
r2y = 22*cos(36) = 17.8 km
a) the second team's distance from the first team,
delta_r = r2 - r1
= (r2x i + r2y j) - (r1x i + r1y j)
= (r2x - r1x)i + (r2y - r1y) j
= (12.9 - (-31.9)) i + (17.8 - 7.2) j
= 44.8 i + 10.6 j km
|delta_r| = sqrt(44.8^2 + 10.6^2)
= 46.04 km
b) second team's direction,
theta = tan^-1(10.6/44.8)
= 13.3 degrees north of east