Question

A stealth blimp leaves its secret base in Nebraska and flies 165 km at 68.0 ∘ east of north and then changes direction to fly 245 km at 48.0 ∘south of east, after which it makes an immediate emergency landing in a corn field.

1. When the airport sends out a rescue crew, how far should this crew fly to go directly to the blimp?

2. In which direction? (Express your answer as an angle measured south of east)

Answer 1

here,

taking north as +y axis and east as +x axis

displacement 1 , d1 = 165 * ( sin(68) i + cos(68) j)

d1 = 153 km i + 61.8 km j

displacement 2 , d2 = 245 * ( cos(48) i - sin(48) j)

d2 = 163.94 km i - 182.1 km j

the net displacement , d = d1 + d2

d = 316.94 km i - 120.3 km j

1)

|d| = sqrt( 316.94^2 + 120.3^2)

|d| = 339 km

the airport sends out a rescue crew for a distance of 339 km

2)

theta = arctan( -120.3 /316.94)

theta = 19.12 degree

the direction is 19.21 degree south of east