PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Two luggage carts, X and Y, are pushed along the same long, straight airport corridor. The positive x-direction is defined as to the right.
Cart X undergoes three consecutive one-dimensional displacements: +8 m, –3 m, and –6 m.
Cart Y is modeled on a whiteboard by a student who draws a 5.0 cm-long arrow pointing to the right to represent a +10 m displacement. The student’s drawing therefore uses the scale 0.50 cm of arrow length to represent 1.0 m of displacement.
After the drawing is completed, Cart Y is actually pushed an additional –4 m along the corridor.
(a) For Cart X, select a scale of your choice and create a complete arrow diagram on a number line showing each of the three individual displacements in the order they occur. On the same diagram, draw the single arrow that represents Cart X’s resultant displacement.
(b) Determine the algebraic value of Cart X’s resultant displacement and state its direction relative to the origin.
(c) Using the student’s original scale for Cart Y, calculate the length and direction of a new arrow that would represent Cart Y’s total displacement after the additional –4 m motion. Show your reasoning.
(d) Compare the final positions of Cart X and Cart Y with respect to the origin. Indicate which cart is farther from the origin and in which direction. Support your answer with both graphical evidence from your drawings and algebraic calculations.