Ch 03: Vectors and Coordinate Systems
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Problem 3
Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of (a) E and FProblem 3
The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. a. What is the particle's distance from the origin at t = 0, 2, and 5 s?Problem 3
The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. b. Find an expression for the particle's velocity v as a function of time.Problem 3
The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. c. What is the particle's speed at t = 0, 2, and 5 s?Problem 3
A cannonball leaves the barrel with velocity v = (75î ＋ 45ĵ). At what angle is the barrel tilted above horizontal?Problem 3
What are the x- and y-components of vector shown in FIGURE EX3.3 in terms of the angle and the magnitude E?
Problem 3
Let E = 2i + 3j and F = 2i - 2j. Find the magnitude of (c) -E - 2FProblem 3
Trevon drives with velocity v₁ = (55î ─ 10ĵ) mph for 1.0 h, then v₂ = (20î ＋ 50ĵ) mph for 2.0 h. What is Trevon's displacement? Write your answer in component form using unit vectors.Problem 3
A runner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. The runner starts at (x,y) = (50m, 0m) and runs 2.5 times around the track in aclockwise direction. What is his displacement vector? Give your answer as a magnitude and direction.Problem 3
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?Problem 3
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?Problem 3
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.Problem 3
FIGURE P3.26 shows vectors A and B. Find D = 2A ＋B Write your answer in component form.
Problem 3
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?
Problem 3
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?Problem 3
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?Problem 3
FIGURE P3.43 shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard and in what direction must you pull on the third rope to keep the knot from moving? Give the direction as an angle below the negative x-axis.
Problem 3
What are the x- and y-components of the velocity vector shown in FIGURE EX3.20?
Problem 3
Let B = (5.0 m, 30 degrees counterclockwise from verically up). Find the x- and y- components of B in each of the two coordinate systems shown in FIGURE EX3.21.
Problem 3
Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jill's velocity vector was 2.5 m/s. b. What was the vertical component of Jill's velocity?Problem 3
A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?Problem 3
Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls with a force of 550 N, what are the horizontal and vertical components of his force? (Force is measured in newtons, abbreviated N.)Problem 3
Trace the vectors in FIGURE EX3.1 onto your paper. Then find (a) A + B
Problem 3
Trace the vectors in FIGURE EX3.1 onto your paper. Then find (b) A - B
Problem 3
Let A = 4i - 2j, B = -3i + 5j, and C = A + B. (a) Write vector C in component form.Problem 3
Let A = 4i - 2j, B = -3i + 5j, and F = A - 4B. (c) What are the magnitude and director of vector F?Problem 3
Four forces are exerted on the object shown in FIGURE P3.45. (Forces are measured in newtons, abbreviated N.) The net force on the object is Fₙₑₜ = F₁ + F₂ + F₃ + F₄ = 4.0î N. What are (a) F₃ and (b) F₄? Give your answers in component form.
Problem 3
A cannon tilted upward at 30° fires a cannonball with a speed of 100 m/s. What is the component of the cannonball's velocity parallel to the ground?Problem 3
b. Use geometry and trigonometry to determine the magnitude and direction of G = E＋F.
Problem 3
Find a vector that points in the same direction as the vector ( î ＋ ĵ ) and whose magnitude is 1.
