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Assessment 1.
Topic: Vector Analysis
Show your complete solutions. Include necessary diagrams.
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- A particle moves along a path, and its speed increases with time. (i) In which of the following cases are its acceleration and velocity vectors parallel? (a) when the path is circular. (b) when the path is straight. (c) when the path is a parabola. (d) never. (ii) From the same choices, in which case are its acceleration and velocity vectors perpendicular everywhere along the path?b. i. Find the vector R that is directed from a point p ( x,, Y1, Z1) to a point e ( *2,Y2, z2) where 7, and 72, Are the position vector. ii. Determine the resultant of i. V4 – Vị + Vs + V½ – V3 ii. V3 + Vị + V¼ – V3 + V2 when vị = 8 units at 70°, v2 = 20 units at 140° and v3 = 15 units at 150°. v4 22 units at 230°,v5 = 18 units at 100°,Three vectors A, B, and C. A = 5.0 m, towards 60 degrees below +x B = 6.0 m, towards +y C = 1.0 m, towards -x A is crossed with B and then dotted with C. Determine the final answer. a. no answer O b.30.0 m^3 O c. 15.0 m^3 O d.0.0 m^3
- 4. What is the angle between vectors A and -A when they are drawn from a common origin? A. 0° В. 45° C. 90° D. 180° 11. A duck flies 10 m/s due south against a gust of wind with a speed of 2.5 m/s. What is the resultant velocity of the duck? A. 7.5 m/s, north B. 7.5 m/s, south C. 12.5 m/s, north D. 12.5 m/s, south 17. What method will you use to solve the resultant vector if the two vectors form 90° with each other? A. Addition 18. Which of the following measurements is categorized as vector? A. 10 N B. Multiplication C. Pythagorean Theorem D. Subtraction В. 47°с C. 64 Gb D. 75 km/h For questions # 19-20: Consider the following displacement vectors: dı= 4.5 km due north d2=6.9 km due north d3=3.5 km due south da=4.5 km due south 19. What is the value of di + d3? C. 1.5 km due south D. 7.5 km due north-south A. -1.5 km due south B. 1.5 km due north 20. What is the value of di + d2 + da? A. 6.9 km due north C. 11.4 km due north D. 15.9 km due north-south B. 6.9 km due southDetermine the equivalent directions for the given vectors.a. 35° N of E b. 20° W of S c. S 40° E d. N 65° W1. Three vectors are given by, R = 2î + 3j – 6k, R2 = 21 – mj – 8k and R3 = nî + 4.5j – 9k Explain why R, & R2 are not parallel to each other. R || R3 & 2|R2 x R3| = [R, . (R2 × R3 )] + v58.8n, calculate the value of m. Calculate the angles that the vector (R, – R2) makes with î, ĵ & k axis. (b)
- 35.0° above the ground. a. How much time does it take for the ball to reach the goal posts? b. How high is the ball when it reaches the goal posts? Does it clear the horizontal bar, which is 3.44m high offa. Vector 'a' has magnitude 5.0m and is directed east. T 2 Vector 'b' has magnitude 4.0m and is directed 350 west of north. What are (a) the magnitude and (b) the direction of 'a +b'? d. Is it possible for a body moving on a circular track to have zero acceleration? Explain vividly if Yes or No e. An electron moving along the x axis has a position given by is the electron from the origin when it momentarily stops? x = (16tet) m, where t is in seconds. How far DizamQ/ A particle moves in an xy plane according to x(1)= -20.00 + 20.00t - 4.00 and y(t) = 25.00 + 17.00t -19.00², with x and y in meters and t in seconds. At t= 10 s, a. What is the particle velocity vector vì nunit vector notation? b. What is the particle acceleration vector đìn unit vector notation?
- 5.3. a. Two position vectors are seen. Draw the displacement 2- on a separate sheet. HELP: Use the tip-to-tip drawing rule 7₂ b. Suppose has magnitude 6 and 2 has magnitude 2. What is the magnitude of Ar=2-71 c. Two velocity vectors are seen. Draw the difference 2-₁. Suppose ₁ has magnitude 5 and 2 has magnitude 10. What is the magnitude of A? 32 V1 IFrom the three vectors V₁ = 4.0i - 8.0j, V₂ = i + j, and V3 = -2.0i + 4.0j. Determine the magnitude of V1 - V2 + V3. A. 4.2 B. 26 OC. 9 OD. 5.11. Mimi is traveling 62m 12° South of East and then 37m 8° West of North. At the end of this journey, she asks you for help. A. What is her resultant vector? B. How far and in what direction do you tell her to go so that she can get back to her initial position?