/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 A bicycle travels \(3.2 \mathrm{... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 33

A bicycle travels \(3.2 \mathrm{km}\) due east in \(0.10 \mathrm{h}\), then $4.8 \mathrm{km}\( at \)15.0^{\circ}\( east of north in \)0.15 \mathrm{h},$ and finally another \(3.2 \mathrm{km}\) due east in \(0.10 \mathrm{h}\) to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?

Short Answer

Expert verified
Answer: The average velocity for the entire trip is approximately 31.863 km/h.

Step by step solution

01

Calculate the displacement for each part of the trip

To calculate the displacement of each part of the trip, we need to find the horizontal (x) and vertical (y) components of the displacement for each part, and then add them up. For the parts where the bicycle is moving due east, the entire displacement is in the x-direction. When moving at an angle, we can use trigonometry (sine and cosine functions) to find the x and y components of the displacement.
02

Calculate horizontal and vertical displacement components for the second part of the trip

For the second part of the trip, the bicycle is traveling 4.8 km at an angle of 15 degrees east of north. To find the x and y components of this displacement, we can use the sine and cosine functions: x = 4.8 * cos(15) = 4.8 * 0.9659 = 4.6365 km y = 4.8 * sin(15) = 4.8 * 0.2588 = 1.2422 km
03

Calculate the total displacement in the x and y directions

To find the total displacement, we can simply add up the displacements in the x and y directions for each part of the trip: Total x displacement = 3.2 + 4.6365 + 3.2 = 11.0365 km Total y displacement = 0 + 1.2422 + 0 = 1.2422 km
04

Calculate the magnitude of the total displacement

To find the magnitude of the total displacement, we can use the Pythagorean theorem: Total displacement = sqrt((total x displacement)^2 + (total y displacement)^2) Total displacement = sqrt((11.0365)^2 + (1.2422)^2) = sqrt(122.8035 + 1.5435) = sqrt(124.3471) = 11.152 km
05

Calculate the total time taken for the trip

The total time taken for the trip is the sum of the times taken for each part of the trip: Total time = 0.10 h + 0.15 h + 0.10 h = 0.35 h
06

Calculate the average velocity for the entire trip

To find the average velocity, we can divide the total displacement by the total time taken: Average velocity = Total displacement / Total time = 11.152 km / 0.35 h = 31.863 km/h The average velocity for the entire trip is approximately 31.863 km/h.

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Most popular questions from this chapter

Margaret walks to the store using the following path: 0.500 miles west, 0.200 miles north, 0.300 miles east. What is her total displacement? That is, what is the length and direction of the vector that points from her house directly to the store? Use vector components to find the answer.
A pilot wants to fly from Dallas to Oklahoma City, a distance of $330 \mathrm{km}\( at an angle of \)10.0^{\circ}$ west of north. The pilot heads directly toward Oklahoma City with an air speed of $200 \mathrm{km} / \mathrm{h}\(. After flying for \)1.0 \mathrm{h},\( the pilot finds that he is \)15 \mathrm{km}$ off course to the west of where he expected to be after one hour assuming there was no wind. (a) What is the velocity and direction of the wind? (b) In what direction should the pilot have headed his plane to fly directly to Oklahoma City without being blown off course?
Prove that the displacement for a trip is equal to the vector sum of the displacements for each leg of the trip. [Hint: Imagine a trip that consists of \(n\) segments. The trip starts at position \(\overrightarrow{\mathbf{r}}_{1},\) proceeds to \(\overrightarrow{\mathbf{r}}_{2},\) then to \(\overrightarrow{\mathbf{r}}_{3}, \ldots\) then to \(\overrightarrow{\mathbf{r}}_{n-1},\) then finally to \(\overrightarrow{\mathbf{r}}_{n} .\) Write an expression for each displacement as the difference of two position vectors and then add them.]
A gull is flying horizontally \(8.00 \mathrm{m}\) above the ground at $6.00 \mathrm{m} / \mathrm{s} .$ The bird is carrying a clam in its beak and plans to crack the clamshell by dropping it on some rocks below. Ignoring air resistance, (a) what is the horizontal distance to the rocks at the moment that the gull should let go of the clam? (b) With what speed relative to the rocks does the clam smash into the rocks? (c) With what speed relative to the gull does the clam smash into the rocks?
At the beginning of a 3.0 -h plane trip, you are traveling due north at $192 \mathrm{km} / \mathrm{h}\(. At the end, you are traveling \)240 \mathrm{km} / \mathrm{h}\( in the northwest direction \)left(45^{\circ}$ west of north). \right. (a) Draw your initial and final velocity vectors. (b) Find the change in your velocity. (c) What is your average acceleration during the trip?
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