Question

Q7. A plane leaves the airport and flies 68.0° east of north and travels 170 km. Then it changes direction of motion to fly 48.0° south of east, and travels 230 km. Finally, it makes an immediate emergency landing on the ground. When the airport sends out a rescue team, how far the team flies to go directly to this plane? A) 329 knm B) 225 km C) 250 km D) 379 kmm E) 401 km

I know that the answer is a but what are the steps of solving it??

Answer 1

d1 = (170 km)*sin 68 i +(170 km)*cos 68 j

d2 =(230 km)*cos (-48) i +(230 km)*sin (-48) j

resultant d = d1 + d2

=((170 km)*sin 68 +(230 km)*cos (-48)) i +((170 km)*cos 68 + 230 km)*sin (-48)) j

d =(311.52 km )i + (-107.240 km) j

magnitude d =sqrt( (311.52 km )^2+ (-107.240 km)^2)

d =329 km

option A is correct