PLEASE ANSWER ASAP!!!!!!!!!!!!!!!!!!!!!!!

a cross country runner runs 3km due east, 5km due south and 8km south west. what is the runners final displacement and what direction?

East = 3 - 8 cos 45 = -2.66

South = 5 + 8 sin 45 = 10.66
tan angle south of west = 10.66/2.66
so
76 degrees south of west or 14 degrees west of south
d^2 = 2.66^2 + 10.66^2
so
d = 11 km

in true bearing that would mean?

No answer

To find the runner's final displacement and direction, we can break down the motion into horizontal and vertical components. Here's how you can calculate it:

1. Draw a diagram: Draw a coordinate plane and mark the positions of the runner's three movements — 3 km east, 5 km south, and 8 km southwest. Label these points A, B, and C, respectively.

2. Calculate the horizontal displacement: From point A to point B, the runner moves only in the vertical direction (south), so the horizontal displacement is 0 km.

3. Calculate the vertical displacement: From point A to point B, the runner moves 5 km south. From point B to point C, the runner moves southwest, which can be resolved into two components: a 5 km vertical displacement (south) and a 3 km horizontal displacement (west). Therefore, the total vertical displacement is 5 km - 5 km = 0 km.

4. Calculate the final displacement: With a horizontal displacement of 0 km and a vertical displacement of 0 km, the runner's final displacement is 0 km.

5. Determine the direction: Since the displacement is 0 km, the direction is undefined or simply referred to as "no direction" or "stationary."

In summary, the runner's final displacement is 0 km with no specific direction.