Question

Three displacements are A=200 m due south, B=250 m due west, and C= 150 m at 30.0° east of north. (a) construct a separate diagram for each of the following possible ways of adding these vectors: R1 = A+B+C ; R2 = B+C+A ; R3 = C+B+A. (b) explain what you can conclude from comparing the diagrams.

Answer 1

here three vectors are given as

$\vec A = 200 (-\hat j)$

$\vec B = 250 (- \hat i)$

$\vec C = 150 cos30 (\hat i) + 150 sin30 (\hat j)$

$\vec C = 130 \hat i + 75 \hat j$

now we will find the sum of all three

$\vec A + \vec B + \vec C = 200 (-\hat j) + 250 (- \hat i) + 130 (\hat i) + 75 (\hat j)$

$R = -120 \hat i -125 \hat j$

so its magnitude will be

$R = \sqrt{120^2 + 125^2}$

$R = 173.3$

So here this resultant will be same in all three cases as it will have same figure in all cases

Answer 2

(a) The diagrams can be seen in the picture attached

(b) By comparing the diagrams we can conclude that the resultant R₁ = R₂ = R₃

Further explanation

Vector is quantity that has magnitude and direction.

One example of a vector is acceleration.

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem !

This problem is about Vector and Vector Diagram.

Given:

Vector A = -200 j

Vector B = -250 i

Vector C = (150 sin 30.0°) i + (150 cos 30.0°) j = 75 i + 75√3 j

Unknown:

R₁ = A + B + C = ?

R₂ = B + C + A = ?

R₃ = C + B + A = ?

Solution:

R₁ = A + B + C  = (-200 j) + (-250 i) + (75 i + 75√3 j)

R₁ = -175i + (75√3 - 200)j

R₂ = B + C + A = (-250 i) + (75 i + 75√3 j) + (-200 j)

R₂ = -175i + (75√3 - 200)j

R₃ = C + B + A  = (75 i + 75√3 j) + (-250 i) + (-200 j)

R₃ = -175i + (75√3 - 200)j

From the results above, it can be concluded that the resultants above produce the same results. This can be confirmed from the diagrams in the attachment.

Learn more

• Velocity of Runner : https://brainly.com/question/3813437
• Kinetic Energy : https://brainly.com/question/692781
• Acceleration : https://brainly.com/question/2283922
• The Speed of Car : https://brainly.com/question/568302

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Stream , Vector