**Problem Description:**Consider a map oriented so that the x-axis runs east-west (with east being the "positive" direction) and the y-axis runs north-south (with north "positive"). A person drives 28 km to the north, turns and drives 73 km to the east, and then turns north and drives for an unknown distance \( z \). If his final position is 97 km from where he started, find \( z \).**Solution:**Let’s represent the movement in a coordinate system. Starting from the origin:1. Move 28 km north: The coordinates are (0,28).2. Move 73 km east: The coordinates become (73, 28).3. Move \( z \) km north: The coordinates are (73, 28 + \( z \)).We use the distance formula to find \( z \):Given the final distance from the start to end is 97 km, we have:\[\sqrt{(73 - 0)^2 + ((28 + z) - 0)^2} = 97\]Simplifying,\[\sqrt{73^2 + (28 + z)^2} = 97\]Squaring both sides,\[73^2 + (28 + z)^2 = 97^2\]Calculating,\( 5329 + 784 + 56z + z^2 = 9409 \)Rearrange terms to form a quadratic equation:\( z^2 + 56z + 6113 = 9409 \)\( z^2 + 56z - 3296 = 0 \)Solving this quadratic equation results in the value of \( z \).

Answered: Image /qna-images/answer/44d1c3f6-6dd3-4845-a0b7-17e745a6a11d.jpg

Consider a map oriented so that the x-axis runs east-west (with east being the "positive" direction) and y runs north-south (with north "positive"). A person drives 28 km to the north, turns and drives 73 km to the east, and then turns north and drives for an unknown distance z. If his final position is 97 km from where he started, find z. km

Consider a map oriented so that the x-axis runs east-west (with east being the "positive" direction) and y runs north-south (with north "positive"). A person drives 28 km to the north, turns and drives 73 km to the east, and then turns north and drives for an unknown distance z. If his final position is 97 km from where he started, find z. km

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: An explorer walks 19km due east, then 15km north, and finally 4km west. A) What is the total…

Q: A car on Cass Ave. is proceeding north, towards Warren Ave., at the rate of 20 miles per hour. A…

A: Given: The speed of car, V = 20 mph The speed of truck, v = 30 mph The position of car, y = 0.4 m…

Q: Graph a scale drawing and determine graphically the magnitude and direction of the fourth…

A: Analyze the following figure. Here, A, B, C, and D represent the first, second, third, and fourth…

Q: Suppose you walk 15.5 m straight west and then 26 m straight north. How far are you, in meters,…

Q: A river flows in a straight line from East to West. Two friends Jack and Jill live on the same side…

A: Displacement shortest distance between initial and final position is called displacement.

Q: Suppose you went for a drive along a long, straight road that runs east-west. Let's define east to…

Q: Transcribed image text: 1. A small plane takes off from the island of Pango and flies for 90.0…

A: Given,1. Flight from Pango to Tango:- Time: 90.0 minutes = 1.5 hours- Speed: 250 MPH- Direction: 15…

Q: John is walking around cam alks 1.45 km west. Finally, Jc - What is the magnitude and

A: The John walks 2.4 km north I'm then making a left turn and walking 1.45 km west. John makes a…

Q: Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0…

Q: Inga is walking near the Circular Forest, a forest in the shape of a circle with a radius of 10 km.…

Q: The First Friday Parade route runs 1,032 m East along the Avenue of Champions then turns North 1,986…

A: Consider the figure.

Q: Figure shows a map of Olivia’s trip to a coffee shop. She gets on her bike at Loomis and then rides…

Q: Jill's dog Sparky runs 50.0 m northeast to a tree, then 90.0 m west to a second tree, and finally…

A: Given: Displacement along northeast direction is 50 m Displacement along west is 90 m Displacement…

Q: You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West…

Q: Erica is participating in a road race. The first part of the race is on a 2.6-mile-long straight…

Q: Vector A⃗ points in the negative y direction and has a magnitude of 5 units. Vector B⃗ has twice…

A: The expression for the vector representation of (A+B):

Q: A student went to Wonderland, where they lined up for the Leviathan roller coaster. After waiting 2…

A: To calculate from Displacement-time graph, Draw a tangent at the point at which instantaneous…

Q: You walk 60 meters to the North and 60 meters to the West. Find the magnitude, direction, and sense…

A: d1 = 60 m (north)d2 = 60 m west magnitude of displacement = 602 + 602 = 602 m = 84.85 m DIrection =…

Q: Suppose you first walk A=35 m in a direction of 20 degrees west of north and then B=58 m in a…

Q: To get to his office from home, Greg walks 5 blocks north and then 2 blocks east. After work he…

A: Step 1: Step 2: Step 3: Step 4:

Q: A high-tech drone flies over Miami, FL in a direction 57.3° west of north with a speed of 34.6 km/h.…

Q: A high-tech drone flies over Miami, FL in a direction 58.3° west of north with a speed of 30.2 km/h.…

A: Let v1 and v2 be the drone’s speed during the fly 58.30 west of north and due north respectively.…

Q: A U.S. Navy destoyer on patrol travels the following displacements starting from coordinate origin.…

Q: The parade runs north for 1.8 mi then heads 20 degrees S of east for 1.4 miles. What is the…

Q: Jane leaves her house and walks 5.0 blocks east and then proceeds north until she is 7.8 blocks from…

Q: A dog walks due East for 10.5 meters, then turns around and walks due West for 6.0 meters. What is…

Q: Ruth sets out to visit her friend Ward, who lives 60 mimi north and 100 mimi east of her. She starts…

A: 1)Write the position vector of Ruth.Write the initial position vector of Ward.

Q: Part A In what direction should the crew fly to go directly to the field? Use components to solve…

A: Solution: The direction and the displacement of the plane are shown by the vector representation on…

Q: A car travels 25km due north and 50km in a direction 35° north of east. X component of the resultant…

Q: Suppose you walk 23.5 m straight west and then 19m straight north for a total magnitude of 30m. A.…

A: Solution: Given: x = distance walked along negative x axis = -23.5 m y = distance walked along…

Q: While exploring a cave, an explorer starts at the entrance and moves the following distances. She…

A: Given Data: Here, the given data is represented in the following diagram. Fig 1. Displacement of…

Q: Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0…

Q: Most days after lunch, I like to take a stroll around campus ( given it’s not too hot ). Suppose on…

Q: (b) What is the y-component of the average velocity of the plane during the second leg of the trip,…

A: Velocity of the plane while traveling to the north east to city B. Hence plane travel from East (+x…

Q: Morty is supposed to meet up with Rick, who is 50 mi north and 100 mi east of Morty,after exploring…

Q: Vector a has magnitude 5.0 m and is directed east. Vector b has magnitude 4.0 m and is directed 35◦…

Concept explainers

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Problem Description:**

Consider a map oriented so that the x-axis runs east-west (with east being the "positive" direction) and the y-axis runs north-south (with north "positive"). A person drives 28 km to the north, turns and drives 73 km to the east, and then turns north and drives for an unknown distance \( z \). If his final position is 97 km from where he started, find \( z \).

**Solution:**

Let’s represent the movement in a coordinate system. Starting from the origin:

1. Move 28 km north: The coordinates are (0,28).
2. Move 73 km east: The coordinates become (73, 28).
3. Move \( z \) km north: The coordinates are (73, 28 + \( z \)).

We use the distance formula to find \( z \):
Given the final distance from the start to end is 97 km, we have:

\[
\sqrt{(73 - 0)^2 + ((28 + z) - 0)^2} = 97
\]

Simplifying,
\[
\sqrt{73^2 + (28 + z)^2} = 97
\]

Squaring both sides,
\[
73^2 + (28 + z)^2 = 97^2
\]

Calculating,
\( 5329 + 784 + 56z + z^2 = 9409 \)

Rearrange terms to form a quadratic equation:
\( z^2 + 56z + 6113 = 9409 \)
\( z^2 + 56z - 3296 = 0 \)

Solving this quadratic equation results in the value of \( z \).

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: Determine the given information

VIEW

Step 2: Derive the expression of final displacement

VIEW

Step 3: Calculate the value of z

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A teenager walks 191 meters north to their friends house and gets therelin 5 min. They forgot their phone so they run back to there house and return to there friends house in 9.8 minutes. If north is considered positive and south is considered negative, what is the total distance of the teenage when they return to their friend's house from the beginning of the trip?
You go on a hike with some friends. First, you travel 1.7 miles in a direction due west. Then, you spend some time checking Twitter and not paying attention to where you're walking. Once you look back up from your phone, you are at a ranger station that is 2.1 miles in a direction 27 degrees west of north from your starting point. How far, and in what direction, did you travel while checking Twitter?
George runs the football 40 yards downfield before he is tackled. The straight line distance between where he began the run and where he was tackled is 18 yards and makes a 25 degree angle with the right sideline. a. What was George's distance traveled in yards? b. What was George's resultant displacement in yards? PIck answer BELOW a. distance = 58yds, displacement = 18yds b. distance = 40yds, displacement = 22yds c. distance = 40 yds, displacement = 18yds d. distance = 18yds, displacement = 40yds
Component Method: With your calculator, determine the x and y components of F1 and F2. Remember that Fx = Fcos θ and Fy = F sin θ. Find the x and y components of the resultant from the sum of x and y components. Draw a right triangle with x and y components as sides, and the hypotenuse representing the resultant. Calculate the magnitude of the resultant from the square root of (Rx2 + Ry2). Calculate the direction of the resultant by using θ R = tan-1 (Ry/Rx).
Pls help ASAP
A driver takes a wrong turn at an intersection and travels 2.6 km north, then 8.7 km east and finally 7.5 km south. What is his displacement from the intersection? Enter your answers without units, correct to three significant digits. (a) The magnitude of the displacement is: This question accepts numbers or formulas. Help | Switch to Equation Editor | Preview (b) The direction of the displacement is: Enter your answer in standard position as an angle in degrees such that 0º < 0< 360°
Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 101 m at an angle 30.0° north of east, and finally moves 184 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east.) Cave entrance W S E Final position What is the resultant displacement from the entrance? magnitude direction m ° south of east
Can you go step by step.
A student bikes to school by traveling first N = 1.00 miles north, then W = 0.400 miles west, and finally S = 0.200 miles south. a. If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance would the bird cover? b. Finally, find ϕ, the angle north of west of the path followed by the bird.
The vector A has a magnitude of 4.0 meters and points in the -x direction. The vector B has a magnitude of 3.0 meters and points in the +y direction. Vector C is deﬁned so that C - A + B = 0. What is the magnitude and direction of vector C? Give your answers to 2 signiﬁcant ﬁgures.
Mariana finds a cave to explore. Starting at the cave entrance, Mariana first follows a passage 75.0 m north, then turns and moves 250 m east, then goes 113 m at an angle 30.0° north of east, and finally moves 179 m south. Find the resultant displacement from the cave entrance. Shown is a sketch of the situation not drawn to scale. (Give the magnitude of the displacement in m and the direction in degrees south of east.) Cave entrance W m N E o south of east 8 What is the resultant displacement from the entrance? magnitude direction Final position Q
An airplane undergoes the following displacements: First, it flies 287 km in a direction 40.6° east of north. Next, it flies 406 km due south. Finally, it flies 69.3 km 24.1° north of west. How far, d, does the airplane end up from its starting point? d km Report your numerical answer below, assuming three significant figures.