constant speed on a track A track is shown in the shape of a 45-45-90 triangle with smooth corners. A 1 kilogram bead is shown moving with a constant speed (8 m/s) on this track. Two points of interest are indicated as "A" and "B". IM Direction Kay The "direction key" shows eight arrow directions labeled 1 to 8. To use the "direction key", consider the vector mentioned in each question. Match the direction of the vector with the arrow in the key that best shows the direction of the required vector.

constant speed on a track A track is shown in the shape of a 45-45-90 triangle with smooth corners. A 1 kilogram bead is shown moving with a constant speed (8 m/s) on this track. Two points of interest are indicated as "A" and "B". IM Direction Kay The "direction key" shows eight arrow directions labeled 1 to 8. To use the "direction key", consider the vector mentioned in each question. Match the direction of the vector with the arrow in the key that best shows the direction of the required vector.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 91CP: between points in a plane do not change when a coordinate system is rotated In other words, the...

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between points in a plane do not change when a coordinate system is rotated In other words, the magnitude of a vector Is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle to become a new coordinate system S’, as shown in the following figure. A point in a plane has coordinates (x,y)in S and coordinates (x,y) in S’. (a) Show that, during the transformation of rotation, the coordinates in S are expressed in terms of the coordinates in S by the following relations: {x=xcos+ysiny=xsin+ycos (b) Show that the distance of point Pto the origin is invariant under rotations of the coordinate system. Here, you have to show that x2+y2=x2+y2. (c) Show that the distance between points Pand Q is invariant under rotations of the coordinate system. Here, you have to show that ( xP =xQ )2+( yP yQ )2=( xP =xQ )2+( yP yQ )2 .
Given the vectors in the preceding figure, find vector Rthat solves equations (a) D+R=Fand (b) D-2D+5R=3F . Assume the +x -axis is horizontal to the right.
crocodiles X and Y start to crawl at the same time wifh equal speeds from a hole to find food. crocodile X starts at 8 m north of east; then goes 10 m 40 degrees S of E; then felt something moving 9 meters North from where it is and moves to it; while crocodile Y went straight from the hole to the moving thing. How far and in what direction did crocodi,e Y move to reach the moving thing? Illustrate the vectors
You first walk 10 meters at an angle of 30 degrees East of North. Then,you walk 15 meters at an angle of 45 degrees South of East. Assume that East is +x and North is+y, and assume you started at the origin (0,0). A. Make a graph with x- and y-axes and draw your path on that graph (to scale, or at least asclose as you can get). Start the first vector at the origin, and the second vector at the tip ofthe first vector. Then, draw the resultant vector (their sum). B. Break each part of the walk into their x- and y-components and then sum them to get thex- and y-components of the resultant vector. Make sure to include units and unit vectors. C. What is your displacement from where you originally started? D. If the whole walk took 40 seconds, then what was your average velocity
In a total time of 3.0 minutes, a duck on a pond paddles 31 m [N33oE] and then paddlesanother 57 m [E28oS]. Solve for the displacement graphically (with a ruler andprotractor) and then answer the questions. The scale diagram should have a scale, labeled axes, correct vector length and directions, vectorlabels, appropriate significant digits based on your measuring device and final answer withmagnitude to correct sig figs, with unit and direction. Using the displacement you determined from your graph, what was the duck’s average velocityfor the trip? What total distance did the duck travel? What was the average speed of the duck for the whole trip?
crocodile X and Y start to crawl at the same time at an equal speed from a hole to find food. crocodile X starts at 8 m NE; then goes 10 m 40o S of E; then felt something moving 9 m N from where it is and moves to it; while crocodile Y went straight from the hole to the moving thing. How far and in what direction did crocodile Y move to reach the moving thing? (Please give the vector illustration)
I need help answering this quadratic word problem, thanks in advance At the national spitting competition, contestants were lined up on top of a tall building. The winning projectile was projected off the top of the building in a trajectory defined by the following equation where the height (h) is in metres above the ground and time (t) is in seconds since the projectile was launched. h=-4.9t^2+29.4t+37.9 Show all work when answering the following (no guess and check allowed): a) If the mouth of the person who launched the winning projectile was 1.6 metres above the roof of the building, how tall was the building? b) To the nearest tenth of a second, how long was the projectile in the air before it hit the ground? (Nearest tenth of a second = one decimal place) c) To the nearest tenth of a second, determine how long the projectile was at or above 80m in height.
A= 150g, 45 degrees B=200g, 0 degrees C= 150g, 270 degrees 1. Record you’re given values of the vectors A,B, and C 2 perform the addition of your vectors the graphical method. Measure the length of R, convert this value back into the resultant in gf units, and find the direction tetaR “i’m wondering if we first need to change the grams to gf by multiplying the mass times 9.8 m/s2, which will Be in N and then change it again to gf”
A roller coaster moves 2.00 x 102 ft horizontally and thenrises 135 ft at an angle of 30.0° above the horizontal. Next, ittravels 135 ft at an angle of 40.0° below the horizontal. Usegraphical techniques to find the roller coaster’s displacementfrom its starting point to the end of this movement.
A plane flies from base camp to lake A, a distance of 280 km at a direction of20.0° north of east. After dropping off supplies, the plane flies to lake B, which is190 km and 30.0° west of north from lake A. Graphically determine the distanceand direction from the base camp to lake B. Then, check your answer using thecomponent method of vector addition.
For each of the following, state whether it is vector, scalar and meaningless. Justify your answers.
Golf shot A golfer stands 390 ft (130 yd) horizontally from thehole and 40 ft below the hole (see figure). Assuming the ball is hitwith an initial speed of 150 ft/s, at what angle(s) should it be hitto land in the hole? Assume the path of the ball lies in a plane.