A plane takes off in san francisco at noon and flies toward the southeast. an hour later, it is 400 kilometers east and 300 kilo

Question

1 month ago

5

A plane takes off in san francisco at noon and flies toward the southeast. an hour later, it is 400 kilometers east and 300 kilo

meters south of its starting location. assuming the plane flew in a straight line, how far did it travel? how many degrees south of east did the plane fly?

Physics

1 answer:

Keith_Richards [3.2K] · Answer 1 · 2026-04-10T18:26:10+03:00

This initial stage represents a right triangle. If the aircraft is positioned 400 km to the east and 300 km to the south of the origin while traveling in a straight path, you can form a right triangle with sides measuring 300, 400, and c. You might notice that these dimensions correspond to multiples of the Pythagorean triple 3, 4, 5, meaning that the length of c is 500 km. Alternatively, you would indicate
$c^2 = 300^2+400^2 \\ c = 500$ .

For the second step, assuming I am correctly understanding "degrees south of east," it involves calculating the angle between the horizontal line indicating east and the trajectory of the aircraft. I created a diagram illustrating this (see attached). You could employ a trigonometric function related to one of the angles to find the solution. I selected
$tan(C)= \frac{3}{4} \\ arctan( \frac{3}{4})=36.870$ . Therefore, I deduce that the angle is 37° south of east.