Can Displacement Be Calculated Without Drawing a Scale Diagram?

[Eqlius]

Homework Statement

An orienteer runs 5km east, 4 km south and 1km west. If she completed the course in exactly 1 hour, calculate her displacement from the start.

Homework Equations

There were questions before it I've already answered but I am not sure if I can do this question through calculation, do I need to do a scale drawing because it isn't a triangle?

The Attempt at a Solution

I've drawn the sketch in my book and found distance to be 10km and average speed to be 10km/h.

It also asks for velocity but i can find that once i find displacement. Mind Blank.

 

[ashishsinghal]

Did you find the displacement?
average velocity = displacement/total time

 

[Eqlius]

Yeh I just drew it. 5.7km/h

 

[supratim1]

displacement is sqrt(32)

 

[rwisz]

I would approach this problem by first defining the terms displacement and velocity. Displacement refers to the change in position of an object from its initial to final position, while velocity is a vector quantity that describes the rate of change of an object's displacement over time.

Based on the given information, the orienteer's displacement can be calculated by finding the straight line distance between her initial and final positions. This can be done using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

In this case, we can represent the orienteer's displacement as the hypotenuse of a right triangle, with one side being 5km (east) and the other side being 3km (south + west). Using the Pythagorean theorem, we can calculate the hypotenuse to be approximately 5.83 km. This is the magnitude of her displacement.

To find her velocity, we need to divide the displacement by the time taken, which in this case is 1 hour. Therefore, her velocity would be 5.83 km/h in a direction that is a combination of east and south-west.

In conclusion, the orienteer's displacement from the start is approximately 5.83 km and her velocity is 5.83 km/h in a south-west direction. This can also be represented as a vector with a magnitude of 5.83 km and a direction of 225 degrees from the east direction.