Topic 1.5: Practice Sheet — 2D Vector Addition

Name: _______________________________ Date: _______________ Period: ______

Directions: Show your work for every problem, including a sketch of each vector where helpful. Round answers to 2-3 significant figures. Circle or box your final answer.

Warm-Up Level (straightforward, one-step)

A vector has a magnitude of 10 m/s at 60° above the horizontal. Find its x- and y-components.
A hiker walks 6 km east, then 8 km north. Find the magnitude and direction of the total displacement.

Standard Level (multi-step, matches typical AP Classroom depth)

Vector A is 12 m at 25° above the horizontal. Vector B is 12 m at 25° below the horizontal. Find the magnitude and direction of the resultant A + B.
A boat experiences a 7 N force east and a 24 N force north at the same time. Find the magnitude and direction of the net force.
A wind velocity is 15 m/s directed 40° north of west. Find its x- and y-components. (Use east as positive x, north as positive y.)

AP-Level (multi-part: calculate + justify/represent/predict-a-change)

A hiker walks 6 km at 50° north of east, then 4 km at 30° west of north. a) Find the total displacement (magnitude and direction). b) Which component total (x or y) contributes more to the resultant's magnitude? Justify using your calculated values. c) If the hiker had instead walked the second leg due west (4 km, straight west) instead of 30° west of north, predict whether the total displacement magnitude would increase or decrease compared to part (a). Explain your reasoning using components, without recalculating the exact new magnitude.
Two vectors have equal magnitude. Under what condition is their resultant's magnitude equal to the SUM of the two magnitudes (the largest possible resultant)? Under what condition is the resultant's magnitude ZERO (the smallest possible)? Explain both using components.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.