Question

Now we'll use the component method to add two vectors. We will use this technique extensively when we begin to consider how forces act upon an object. Vector A has a magnitude of 50 cm and a direction of 30°, and vector B has a magnitude of 35 cm and a direction of 110°. Both angles are measured counterclockwise from the positive x axis. Use components to calculate the magnitude and direction of the vector sum (i.e., the resultant) R = A + B. Part A - Practice Problem: Find the magnitude of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the magnitude in meters. Part B - Practice Problem: Find the direction of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the direction in degrees.

          Now we'll use the component method to add two vectors. We will use this technique extensively when we begin to consider how forces act upon an object. Vector A has a magnitude of 50 cm and a direction of 30°, and vector B has a magnitude of 35 cm and a direction of 110°. Both angles are measured counterclockwise from the positive x axis. Use components to calculate the magnitude and direction of the vector sum (i.e., the resultant) R = A + B.

Part A - Practice Problem:
Find the magnitude of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the magnitude in meters.

Part B - Practice Problem:
Find the direction of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the direction in degrees.

Show more…

Now we'll use the component method to add two vectors. We will use this technique extensively when we begin to consider how forces act upon an object. Vector A has a magnitude of 50 cm and a direction of 30°, and vector B has a magnitude of 35 cm and a direction of 110°. Both angles are measured counterclockwise from the positive x axis. Use components to calculate the magnitude and direction of the vector sum (i.e., the resultant) R = A + B.

Part A - Practice Problem:
Find the magnitude of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the magnitude in meters.

Part B - Practice Problem:
Find the direction of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the direction in degrees.

Added by Sharon W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Surjit Tewari

07/11/2022

Step 1

30 cm y component of A = 50 cm * sin(30°) = 50 * 1 / 2 = 25 cm Show more…

Show all steps

lock

Thanks for your feedback!

Now we will use the component method to add two vectors. We will use this technique extensively when we begin to consider how forces act upon an object. Vector A has a magnitude of 50 cm and a direction of 30°, and vector B has a magnitude of 35 cm and a direction of 110°. Both angles are measured counterclockwise from the positive x-axis. Use components to calculate the magnitude and direction of the vector sum (i.e. the resultant) R = A + B. Part A - Practice Problem: Find the magnitude of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the magnitude in meters. Part B - Practice Problem: Find the direction of the vector sum of these two vectors by using components: 45 m, 65°; 80 m, 145°. Express the direction in degrees.

Play audio

Feedback

Powered by NumerAI

Surjit Tewari and 74 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 In the first question the vector a is given as we will write the vector a in unit vector form.

00:12 So vector a is 50 centimeter at 30 degree.

00:16 So 50 into cost 30 degree into i cap plus 50 into 5 .5 into sine 30 degree into j cap.

00:48 Similarly, the vector b can be written in unit vector form is 35 into cost 110 degree into icap plus 35 into sign of 110 degree into j cap.

01:35 Now to find the resultant of these two vectors, we will add the x component of vector a with the x component of vector b and the y component of vector a with the y component of vector b so the resultant of these two vectors will become r is equal to r vector is equal to 31 point 31 .33 into i cap plus 57 .9 into j cap.

02:31 This is the resultant of the two given vectors.

02:36 Now the magnitude of this resultant is r is equal to under root 31 .3 square plus 57 .9 square.

03:03 So we get the magnitude of the resultant is equal to 65 .8 65 .8 cm.

03:28 Now we have to find the direction of this resultant vector.

03:32 So the direction is 3 -ta is equal to 10 inverse.

03:45 Y component, y component is 57 .9 divided by the x component.

03:58 X component is 31 .3.

04:10 So we get the desired direction.

04:14 Ceta is equal to 61 .6 degree.

04:22 This is the required direction...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later