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9/11/2016 HW3 HW3 Due: 11:59pm on Saturday, September 10, 2016 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 3.2 Part A Find C ⃗ = ⃗ ⃗ A +B . ANSWER: Part B Find D⃗ = ⃗ ⃗ A −B . ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 1/10 9/11/2016 HW3 Problem 3.6 Find x­ and y­components of the following vectors. Part A ∘ r ⃗ = (150m, 45 below positive x − axis) Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: rx , ry = m Part B ∘ v ⃗ = (620m/s, 40 above positive x − axis) Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: vx , v y = m/s Part C 2 a⃗ = (5.8m/s , negative y − direction) Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 2/10 9/11/2016 ax HW3 , ay = m/s2 Problem 3.12 Let A⃗ = 2^ ı + 3^ ȷ and B⃗ = 4^ ı − 2^ ȷ . Part A Plot vectors A⃗ and B⃗ . Draw the vectors with their tails at the origin. ANSWER: Part B This question will be shown after you complete previous question(s). Problem 3.16 Let A⃗ = 7^ ı − 3^ ȷ , B⃗ = −2 ^ ı + 6^ ȷ , and F ⃗ = ⃗ ⃗ A − 4B . Part A ⃗ What is the component form of vector F ? ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 3/10 9/11/2016 HW3 F ⃗ = 15 ^ ı − 27^ ȷ F ⃗ = 9^ ı + 27^ ȷ F ⃗ = 14 ^ ı − 15^ ȷ F ⃗ = −15 ^ ı + 27^ ȷ Part B ⃗ What is the magnitude of vector F ? ANSWER: F = Part C ⃗ What is the direction of vector F ? ANSWER: = ∘ below positive x­axis θ Enhanced EOC: Problem 3.26 The figure shows vectors A⃗ and B⃗ . Find D⃗ = 2.70 A⃗ + B⃗ . You may want to review ( page ) . For help with math skills, you may want to review: Vector Addition Part A Express D⃗ in the form Dx , Dy , where the x and y components are separated by a comma. You did not open hints for this part. ANSWER: ⃗ D = https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 4/10 9/11/2016 HW3 Problem 3.02 Part A Vectors A⃗ and B⃗ are shown in the figure. Vector C⃗ is given by C⃗ = B⃗ ­ A⃗ . The magnitude of vector A⃗ is 16.0 units, and the magnitude of vector B⃗ is 7.00 units. What is the magnitude of vector C⃗ ? ANSWER: 17.5 16.2 15.5 9.00 9.53 Problem 3.42 The figure 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. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 5/10 9/11/2016 HW3 Part A How hard must you pull on the third rope to keep the knot from moving? ANSWER: F = units of force Part B In what direction must you pull on the third rope to keep the knot from moving? ANSWER: = ∘ counterclockwise from the left direction θ Problem 3.20 Part A ^ ⃗ ^ ⃗ ⃗ ^ ^ If A⃗ = + 3 ^i ­ 2 ^ j ­ 4 k and C = ­ 5 i ­2 j ­ 3 k , which of the following numbers is closest to the magnitude of A ­ C? ANSWER: 6 12 8 11 10 Problem 3.32 Jim's dog Sparky runs 45 m northeast to a tree, then 70 m west to a second tree, and finally 20 m south to a third tree. Part A Calculate Sparky's net displacement vector. Enter the east and north components of the net displacement, separated by commas. ANSWER: ⃗ (Dnet ) East ,(D⃗ net )North = m Part B Calculate the magnitude of Sparky's net displacement. Express your answer in meters. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 6/10 9/11/2016 HW3 ANSWER: Dnet = m Part C Calculate the direction of Sparky's net displacement. Express your answer in degrees. ANSWER: θnet = ∘ north of west Problem 3.16 Part A Three forces are exerted on an object placed on a tilted floor. Forces are vectors. The three forces are directed as shown in the figure. If the forces have magnitudes F1 = 1.0 N, F2 = 14.0 N and F3 = 13.0 N, where N is the standard unit of force, what is the component of the net force F⃗ net ⃗ ⃗ ⃗ =F +F2 + F3 parallel to the floor? ANSWER: 5.5 N 10 N 12 N 15 N Problem 3.12 Part A The components of vector A⃗ are A x = +8.7 and A y = ­5.5 , and the components of vector B⃗ are given are Bx = ­4.3 and By = ­3.8. What is the magnitude of the vector B⃗ ­ A⃗ ? ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 7/10 9/11/2016 HW3 10 16 18 13 8.5 Problem 3.20 ⃗ ^ ^ Let E⃗ = 3^i + 3^ j and F = 3 i − 3 j . Part A Find the magnitude of E⃗ . ANSWER: Part B Find the magnitude of F .⃗ ANSWER: Part C Find the magnitude of E⃗ + F .⃗ ANSWER: Part D Find the magnitude of −E⃗ − 2F .⃗ ANSWER: Conceptual Question 3.2 Part A ⃗ ⃗ ⃗ https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 8/10 9/11/2016 HW3 If C ⃗ = ⃗ ⃗ A +B , can C = A+B ? ANSWER: Yes No Part B Can C > A+B ? ANSWER: Yes No Problem 3.08 Part A Vector A⃗ has a magnitude of 5.5 cm and points along the x­axis. Vector B⃗ has a magnitude of 7.5 cm and points at +30° above the negative x­axis. (a) Determine the x and y components of Vector A⃗ . Enter your answers numerically separated by a comma. ANSWER: Ax , A y = cm Part B (b) Determine the x and y components of Vector B⃗ . Enter your answers numerically separated by a comma. ANSWER: Bx , B y = cm Part C (c) Determine x and y components of the sum of these two vectors. Enter your answers numerically separated by a comma. ANSWER: Rx , R y = cm https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 9/10 9/11/2016 HW3 Part D (d) Determine the magnitude of the sum of these two vectors. Enter your answer numerically. ANSWER: R = cm Part E (e) Determine the direction of the sum of these two vectors. Enter your answer numerically. ANSWER: ° above the negative x­axis Problem 3.34 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 . Part A What was the angle of the hill? Express your answer in degrees. ANSWER: = θ ∘ Part B What was the vertical component of Jill's velocity? Express your answer with the appropriate units. ANSWER: vy = Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 150 points. https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=4710744 10/10