Question

calculating displacement practice
displacement in 1 - dimension
directions: galaxy the cat has snuck out of the house to help us visualize displacement by moving different ways around her neighborhood. consider galaxy’s house the origin (0 m). for each scenario, calculate the displacement. use the diagram on the back of this page to visualize the movement.
remember: your answer should have direction and magnitude!

1. galaxy walks 7 meters east from her house to inspect a flower.

what is her displacement?

1. from her house, galaxy walks 8 meters west to hiss at a dog. then she walks another 2 meters west to smell a tree.

what is her total displacement?

1. from her house, galaxy walks 10 meters south to the neighborhood cat hangout spot.

what is her displacement?

1. while at the hangout spot, galaxy sees a cat named link. she walks 3 meters north from the park to verify if link is cool enough to hangout with them.

what is her displacement?

1. galaxy’s friend ziggy is meowing for galaxy to come get her. from the hangout spot, galaxy walks 19 meters north to where ziggy is. then, galaxy and ziggy go back to the hangout spot.

what is her total displacement?
displacement in 2 - dimensions
directions: for each scenario, calculate the displacement. you will need to use the diagram to visualize the movement and to determine how many meters galaxy is moving.
remember: your answer should have direction and magnitude!
pythagorean theorem: $a^{2}+b^{2}=c^{2}\to c = sqrt{a^{2}+b^{2}}$

1. galaxy walks from her house to inspect the tree again, then she catches the scent of some stinky shrubs and walks south to smell them.

what is her displacement from home when she is at the shrubs?
show work!

1. from home, galaxy walks to inspect a pile of trash some hooligan threw in the backyard.

what is her displacement?
show work!

1. from home, galaxy runs to catch a field mouse.

what is her displacement?
show work!

Explanation:

Step1: Define displacement

Displacement is a vector quantity with magnitude and direction from the starting - point to the ending - point.

Step2: Solve problem 1

Galaxy walks 7 meters East. Magnitude is 7 meters and direction is East.

Step3: Solve problem 2

She walks 8 meters West then 2 meters West. Total displacement is \(8 + 2=10\) meters West.

Step4: Solve problem 3

She walks 10 meters South. Magnitude is 10 meters and direction is South.

Step5: Solve problem 4

She walks 3 meters North. Magnitude is 3 meters and direction is North.

Step6: Solve problem 5

She walks 19 meters North then back 19 meters South to the hang - out spot. Net displacement is 0 meters.

Step7: Solve problem 6

Since no information about the horizontal and vertical distances in 2 - D is given for this part, we cannot calculate. Assume we have horizontal distance \(x\) and vertical distance \(y\), then displacement \(d=\sqrt{x^{2}+y^{2}}\) using Pythagorean theorem and direction is \(\tan^{- 1}(\frac{y}{x})\) (angle with respect to the horizontal). But without values, we just note the method.

Step8: Solve problem 7

No information about the position of the trash in 2 - D is given, so we cannot calculate.

Step9: Solve problem 8

No information about the position of the field - mouse in 2 - D is given, so we cannot calculate.

Answer:

1. 7 meters East
2. 10 meters West
3. 10 meters South
4. 3 meters North
5. 0 meters
6. Cannot be calculated without more information
7. Cannot be calculated without more information
8. Cannot be calculated without more information