While vacationing in the mountains you do some hiking. In the morning, your displacement is Sₘₒᵣₙᵢₙ₉ = (2000 m, east) ＋ (3000 m, north) ＋(200 m, vertical). Continuing on after lunch, your displacement is Sₐբₜₑᵣₙₒₒₙ = (1500 m, west) ＋ (2000 m, north) ─ (300 m, vertical). a. At the end of the hike, how much higher or lower are you compared to your starting point?

While vacationing in the mountains you do some hiking. In the morning, your displacement is Sₘₒᵣₙᵢₙ₉ = (2000 m, east) ＋ (3000 m, north) ＋(200 m, vertical). Continuing on after lunch, your displacement is Sₐբₜₑᵣₙₒₒₙ = (1500 m, west) ＋ (2000 m, north) ─ (300 m, vertical). b. What is the magnitude of your net displacement for the day?

Ruth sets out to visit her friend Ward, who lives 50 mi north and 100 mi east of her. She starts by driving east, but after 30 mi she comes to a detour that takes her 15 mi south before going east again. She then drives east for 8 mi and runs out of gas, so Ward flies there in his small plane to get her. What is Ward's displacement vector? Give your answer (a) in component form, using a coordinate system in which the y-axis points north, and (b) as a magnitude and direction.

The bacterium E. coli is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. FIGURE P3.42 shows the trajectory of an E. coli as it moves from point A to point E. What are the magnitude and direction of the bacterium's average velocity for the entire trip?

A velocity vector 40 degrees below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

A position vector in the first quadrant has an x-component of 6 m and a magnitude of 10 m. What is the value of its y-component?