Solve symbolically for y (step 6).
r^(2)=x^(2)-y^(2)->y=+sqrt(r^(2)-x^(2))
Substitute the numbers, with units (step 7).
y=sqrt((525km)^(2)-(4.50 imes 10^(2)(km))^(2))=270km
LEARN MORE
Remarks: Note that the negative solution has been disregarded because it's not physically meaningful. In checking (step 8), note that the units are correct and that an approximate answer can be obtained by using the easier quantities, 500km and 400km. Doing so gives an answer of 300km, which is approximately the same as our calculated answer of 270km.
Question: What is the answer if the distance traveled due east and the direct return distance are both doubled?
Make the appropriate changes in the values used in the example, or else use your knowledge of similar triangles to see quickly what the answer must be.
PRACTICE IT
Use the worked example above to help you solve this problem. An airplane travels 3.90 imes 10^(2)km due east and then travels an unknown distance due north. Finally, it returns to its starting point by traveling a distance of 520km. How far did the airplane travel in the northerly direction?
Your response differs from the correct answer by more than 10%. Double check your calculations. km
EXERCISE
HINTS:
GETTING STARTED
I'M STUCK!
A plane flies 333km due south, then turns and flies 616km at a heading north of east, until it's due east of its starting point. If the plane now turns and heads for home, how far will it have to go?
Reread the problem and make sure you understand all of the given information. A drawing might help you to sort out what is going on here. km
5).
ehrstep
r=x+y
Solve symbolically for y(step 6).
r2=x2-y2-y=+2-x2
Substitute the numbers,with units step 7.
y=v(525 km)2-(4.50x102km)2=270km
LEARN MORE
Remarks Note that the negative solution has been disregarded, because it's not physically meaningful. In checking (step 8), note that the units are correct and that an approximate answer can be obtained by using the easier quantities, 500 km and 400 km. Doing so gives an answer of 300 km, which is approximately the same as our calculated answer of 270 km.
Question What is the answer if the distance traveled due east and the direct return distance are both doubled? 700.24
triangles to see quickly what the answer must be.
PRACTICEIT
Use the worked example above to help you solve this problem. An airplane travels 3.90 x 102 km due east and then travels an unknown distance due north. Finally, it returns to its starting point by traveling a distance of 520 km. How far did the airplane travel in the northerly direction? 616 X Your response differs from the correct answer by more than 10%. Double check your calculations. km EXERCISE HINTS:GETTING STARTED I'M STUCK! A plane flies 333 km due south, then turns and flies 616 km at a heading north of east, until it's due east of its starting point. If the plane now turns and heads for home, how far will it have to go? 700.24 Reread the problem and make sure you understand all of the given information. A drawing might help you to sort out what is going on here.km
