A particle undergoes three consecutive displacements: AT, = (15î + 30j + 12k) cm, Af, = (23 î – 14j – 5.0k) cm, and AT, = (-13î+ 15j) cm. Find unit-vector notation for the resultant displacement and its magnitude.

A particle undergoes three consecutive displacements: AT, = (15î + 30j + 12k) cm, Af, = (23 î – 14j – 5.0k) cm, and AT, = (-13î+ 15j) cm. Find unit-vector notation for the resultant displacement and its magnitude.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 44P: Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units,...

See similar textbooks

Related questions

Q: Vector I is 20.00 km southeast, Z is 14.00 km west, A is 12.50 km 35° W of S, and L is 15.00 km 58°…

A: a) So, the x component of R is Rx=Ix+Zx+Ax+LxRx=20cos45+-14+-12.5 sin…

Q: Vector A = 2.00i+ 3.00j Newtons. Vector B = 4.00 i +1.00 j meters. What is the angle (in degrees)…

A: Lets represent vector A as A and its magnitude as A , similarly vector B as B and its magnitude as…

Q: Let the vector A= 3i -5j +4k and B 7i-8j – 9k.S A-B equal 4i + 3j +13k- 10i- 12) -13k 2 4i - 3) -13k…

A: In the Question we have to given that two vectors A and B then we have to determine the difference…

Q: Consider the vectors A = 6i + 3j and B = 3î - 6j.

Q: Find the speed and direction of an object with v,= 2.0 cm/s and vy= 3.0 cm/s. O 3.6 cm/s, 56° from…

A: Given data: Vx = 2.0 cm/s Vy = 3.0 cm/s Required: The speed and direction of the object

Q: For the vectors u=i+3j+2k and v=2i−2j+2k calculate projvu and scalvu

Q: AB- AB sine, where @ is the angle between the two vectors

A: Remember the vector law and formulas

Q: Consider three displacement vectors A* = (3x - 3ý ) m, B* = ( – 4ỹ ) m,and C* = (-2x + 5ý ) m. The…

A: The displacement vectors are given as A→=3x^-3y^ mB→=x^-4y^ mC→=-2x^+5y^ m

Q: Two vectors are presented as a = 6.0i + 4.5j and b = 5.5î + 2.5j. Find the following. (Hint: For…

A: Given that:a→=6.0i^+4.5j^b→=5.5i^+2.5j^

Q: What is the angle between the vector A = +3i - 2i - 3k and the +y-axis?

A: Given:Vector are,A→=3i^-2j^-3 k^ ...(1)B→=Along y-axisB→=y^=j^ .... (2)We know,cosθ=A→.B→|A||B|…

Q: Two vectors are given by a→=2.8î+7.4ĵ and b→=5.9î+3.7ĵ. Find (a) ||a→×b→||, (b)a→⋅b→,…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Two vectors are given by a = 2.5î + 5.6ĵ and b = 7.9î + 2.4ĵ. Find (a) a × b ,(b) đ b,(c) (a + b). b…

Q: A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on…

Q: = 10 kg at r1 = 75cm m3 = 20 kg at r3 = 25cm m4 = 5 kg at r4 = 50cm 1. Compute the theoretical…

Q: Consider the vectors a = 3i + 2j + 6k and b = −9i − 6j + 2k, where i, j, and k are…

Q: In this question the unit vectors i and j are in the directions east and north respectively. A…

A: The equations of motions can be found using:

Q: Consider the two vectors A = 2.9i - 1.1j and B = -1i - 4.2j a) Calculate A + B 1.90 i -5.30 j b)…

Q: A particle is moving along the x-axis in accordance with the following: x(t) = 5 cos (4πt + π/3)…

A: x(t) = 5 cos (4πt + π/3) cmnow, x = 0 , whenever the cosine term is zero Therefore, cos (4πt + π/3)…

Q: Let V→V→ = 2.00 iˆi^ +6.00 jˆj^ -3.00 kˆk^ . The magnitude of V→V→ is

A: The magnitude of a vector formula is used to calculate the length for a given vector (say v) and is…

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

A: The vector, a→=i^+8j^+4k^ The vector, b→=7i^-6j^-6k^ where i^, j^, k^ are unit vectors in the…

Q: The position of a particle changes from r1= (1.07cm)i+(4.87cm)j to r2=(-4.22cm)i+(4.87cm)j. What is…

Q: 2/2 The magnitude of the force F is 400 lb. Express F as a vector in terms of the unit vectors i and…

A: |F| = 400 lb θ = 30o above -x axis

Q: The scalar product A · B of the two vectors A = 2i + 3j and B = i - 2j is O 8 k O -4 k O 2i - 6j

Q: Given two vectors: M = -3i + 6j – 5k and N= -2i + 3j + k The magnitude of 2N - Mis A 7.07 B 39.2 C…

A: Given: M→=-3i^+6j^-5k^N→=-2i^+3j^+k^

Q: Express the 8.9-kN force F as a vector in terms of the unit vectors i, j, and k. Determine the…

A: Solution: Given That F = 8.9 kN by taking vectors , we can find Fz = 8.9 sin31° Fz = 4.58 kN F' =…

Q: В) 1.63 C) 1.28 D) 1.02 E) 1.84 4) Two vectors, A= 2x+3y and B= 4x-8y. The magnitude of A+B is: A)…

Q: Here are three vectors in meters: d→1=-6.50î+8.40ĵ+9.60k̂ d→2=-2.00î-4.00ĵ+2.00k̂…

Q: Determine the cross product of the following vectors A x B, write the component in the j-direction.…

Q: Consider three vectors A = 15.3i + 1.7j, B = 9.5i + 9.1j, and C = -2.7i - 11.4j. What is the result…

Q: A particle moves along the X-axis. Its velocity (cm/s) versus t(s) is shown below. The magnitude of…

A: In above question we have a histogram The above histogram ( velocity vs time) In above histogram y…

Q: Given vectors P = 4i - 2j + 5k ; Q = -i + 3j - 6k ; find QxP. a. -3i + 19j - 10k b. -3i -19j + 10k…

Q: For the following three vectors, what is 2⋅C→⋅(3A→×B→)? A=300i+300j-300k B=-300i+3.00j+4.00k…

Q: Two vectors are given by A = 3i – 23 + 4k and Ảx B. B = 6j – 2k. Ignoring units, calculate

Q: In a game of pool, ball A is moving with a velocity vo when it strikes balls B and C which are at…

Q: The function s(t) = 64 – 16(t – 1)´ gives the height of a ball in feet for a - given time t in…

Q: For the following three vectors, what is 50 (2 x B)? A = 2.00î + 3.00ĵ – 6.00k B = -3.00î + 2.00ĵ +…

Q: Given two vectors: M = -3i + 6j – 5k and N= -2i + 3j +k The magnitude of 2 – Mis (A 202 B) 7.07 6.08…

Q: 97 PROBLEMS 2-45. Describe how to determine whe ther an equilibrium is stable or unstable when…

A: Taking potential energy (U), and displacement (x). Since equilibrium is the point at which there is…

Q: 38 ao For the following three vectors, what is 3C (2Ā × B)? A = 2.00i + 3.00 – 4.00k B = -3.00i +…

A: The three vectors,

Q: Given two vectors that starts from the origin: A = 2i – 7j and B = I – 3j – 5k. What is the length…

A: Given, OA = 2i - 7 j OB = i - 3 j - 5 k As we know, from the rule of vector addition and…

Q: Consider the two vectors A = 5 î – ĵ and B = - î – 6 j.

A: As the operations in two vectors A→ = a1i⏞ +a2j⏞ and B→ = b1i ^ + b2 6j^A→ + B →=a1+ b1 i^ + a2 +…

Q: A particle undergoes three consecutive displacements d1=(1.5i+3.0j-1.2km) cm, d2=(2.3i-1.4j-3.6k) cm…

Q: Three vectors are given, what is 3C · (2A × B)? A = 2î + 33 – 4k B = -3î + 43 + 2k Č = 7î – 8ĵ

Q: For the following three vectors, what is 3. 7 . (2 Ả × B )? A = 2.00î + 4.00) – 3.00k B = - 3.00î +…

Q: Two vectors are given by a→=4.0î+2.8ĵ and b→=2.1î+7.7ĵ. Find (a) ||a→×b→||, (b)a→⋅b→,…

Q: results from (a) d→1⋅(d→2+d→3), (b) d→1⋅(d→2×d→3), and d→1×(d→2+d→3

A: As per rules... First three parts are posted.

Q: What unit vector is in the same direction as v = 2i - 4j?

A: The vector is given as v→=2i-4j

Q: vector e, in the n- direction and the unit vector e; in the t direction, the acceleration can be…

Q: A particle moves along the X-axis. Its velocity (cm/s) versus t(s) is shown below. The magnitude of…

A: Instantaneous velocity is the velocity at a given time . Slope of position time graph gives…

Question

A particle undergoes three consecutive displacements: AT, = (15î + 30j + 12k) cm, Af, = (23 î – 14j – 5.0k) cm, and
AT, = (-13î+ 15j) cm. Find unit-vector notation for the resultant displacement and its magnitude.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?
A person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At the end of the walk, what is the persons resultant displacement measured from the starting point? Figure P1.51
Given vector A = (3.00i - 2.00j)m and vector B = (-2.00i + 2.00j)m determine vector C if C = 3A - B. Answers should have three significant figures and each component should have units. Remember to leave a space between your numerical values and the units.
What is the magnitude of the vector r=7.9i - 3.0j, where i and j represent the x-and y- unit vectors?
1.53 · Given two vectors A = -2.00î + 3.00î + 4.00k and B = 3.00î + 1.00ĵ – 3.00k, do the following. (a) Find the mag- nitude of each vector. (b) Write an expression for the vector differ- ence A - B using unit vectors. (c) Find the magnitude of the vector difference Á – B. Is this the same as the magnitude of B – Ả? Explain.
Given two vectors A = - 2.00 + 3.00ĵ + 4.00 k and B = 3.00 î+ 1.00 – 3.00 k, (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference A B. Is this the same as the magnitude of B (c) find the magnitude of the vector difference A Explain. B; and A?
An electron's position is given by r=(ti+t2j+2k) with t in seconds and r in meters. A)Determine the electron's velocity v(t) in unit vector notation. B)What is the magnitude of v(t) at t=2 s? C)What is the angle between v(t) and the unit vector ı ?
Given two vectors A= -2.00i + 3.00j +4.00k and B= 3.00i + 1.0oj -3.00k, do the following. (a) Find the magnitude of each vector. (b) Write an expression for the vector difference A - B using unit vectors. (c) Find the magnitude of the vector difference A - B Is this the same as the magnitude of B - A?
Problem 1: Vectors A and B are shown in Figure 1. a. What is A in terms of x and y components? Answer: A = 2.74î +7.52ĵ b. What is B in terms of x and y components? Answer: B = -18.13î - 8.45) c. What is the resultant vector R = A + B? Answer: R= -15.39î - 0.93ĵ d. What is R, the magnitude of R? Answer: R = 15.42 e. What is, the angle R makes with respect to the +x-axis? 0 = 180° +3.46° = 183.46° B Figure 1: Vectors for Problem 1. 25° B = 20 Ā A = 8 /70°
The polar coordinates of a certain point are (r = 2.00 cm, θ = 234°). (a) Find its Cartesian coordinates x and y. x = cm y = cm (b) Find the polar coordinates of the points with Cartesian coordinates (−x, y). r = cm θ = ° (c) Find the polar coordinates of the points with Cartesian coordinates (−2x, −2y). r = cm θ = ° (d) Find the polar coordinates of the points with Cartesian coordinates (3x, −3y). r = cm θ = °
Given two vectors A= -2.0Oi + 3.00j +4.00k and B= 3.00i + 1.0oj -3.00k, do the following. (a) Find the magnitude of each vector. (b) Write an expression for the vector difference A - B using unit vectors. (c) Find the magnitude of the vector difference A - B Is this the same as the magnitude of B – A?
For a given 3-Dimensional vector: A = Axi + Ayj + Azk Its magnitude maybe obtained by product also called the product, expressed as the following A⋅A = Ax2 + A + However, we know that A⋅A = A so A = A2 + Ay + z Then, the magnitude is expressed as: A = sqrt ( Ax2 + A + )