25QUESTION 4ProblemAn explorer in Antarctica leaves his shelter during a whiteout. He takes 50 m northeast, next 180 m at 72° north of west, and then 150 m due south. Save the explorer frombecoming hopelessly lost by giving him the displacement, calculated by using the method of components, that will retum him to his shelter.SolutionBy vector-component approach, we list down the given in a table as follows:X-component (w/ sign direction)y-component (w/ sign direction)GivenA = 50 m NE%3DB 180 m 72° NWmC 150 m S%3DmResultantThus, the magnitude of the resultant vector isR =With a direction ofO NWTherefore, the vector needed for him to successfully get back home isO SERhome =%3DEEEEEEE

Answered: Image /qna-images/answer/7b8dd5a2-ef17-4313-9ee4-afd8c225e7ed.jpg

Answered: QUESTION 4 Problem An explorer in…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter3: Two-dimensional Kinematics

Section: Chapter Questions

Problem 18PE: You drive 7.50 km in a straight line in a direction 15° east of north. (a) Find the distances you...

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Suppose you first walk 12.0 m in a direction 20° west of north and then 20.0 m in a direction 40.0° south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B, as in Figure 3.56, then this problem finds their sum R=A+B. )
You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the balls maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.
Find the following for path D in Figure 3.58: (a) the total distance traveled and (b) the magnitude and direction of the displacement from start to finish. In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.
In a game of American football. a quarterback takes the ball from the line of scrimmage. runs backward a distance of 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a forward pass downfield 50.0 yards perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?
A man in a maze makes three consecutive displacements. His first displacement is 8.00 m westward, and the second is 13.0 m northward. At the end of his third displacement he is back to where he started. Use the graphical method to find the magnitude and direction of his third displacement.
You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the balls maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.
Suppose you take two steps A and B (that is, two nonzero displacements). Under what circumstances can you end up at your starting point? More generally, under what circumstances can two nonzero vectors add to give zero? Is the maximum distance you can end up from the starting point A+B the sum of the lengths of the two steps?
Find the following for path A in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.
Is it possible for two vectors of different magnitudes to add to zero? Is it possible for three vectors of different magnitudes to add to zero? Explain.
You drive 7.50 km in a straight line in a direction 15° east of north. (a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (This determination is equivalent to find the components of the displacement along the east and north directions.) (b) Show that you still arrive at the same point if the east and north legs are reversed in order.
Figure OQ3.3 shows two vectors D 1, and D2. Which of the possibilities (a) through (d) is the vector D2 - 2D1, or (e) is it none of them?
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0° north of east (which is equivalent to subtracting B from A that is, to finding R=AB ). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0° south of west and then 12.0 m in a direction 20.0° east of south (which is equivalent to subtracting A from B that is, to finding R=BA=R ). Show that this is the case.

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