Chapter 1: Q4CP (page 12)

If $\vec{v} = <2, - 3, 5>$ m/s, then what is $|- \frac{1}{2} \vec{v}|$ ?

Short Answer

Expert verified

The value of $|- \frac{1}{2} \vec{v}|$ is 3.08 m/s .

Step by step solution

Understanding the concept of multiplication of vector with a scalar

If a vector is multiplied by a scalar, its corresponding components get multiplied by the scalar individually.The magnitude of a particular vector can be evaluated when its corresponding components are squared and added. Then its square root needs to be found.

Determination of the velocity vector -12v→

The given velocity vector is $\vec{v} = <2, - 3, 5>$ m/s_.

Multiply the given vector by $- \frac{1}{2}$ to get the required velocity vector,

role="math" localid="1653562866807" $- \frac{1}{2} \vec{v} = <- \frac{2}{2}, \frac{3}{2}, - \frac{5}{2}>$ m/s

$= <- 1, \frac{3}{2}, - \frac{5}{2}>$ m/s

Determination of magnitude of -12v→

Take the square root of sum of the squares of all the components of the vectors to obtain the required magnitude,

$|- \frac{1}{2} \vec{v}| = \sqrt{{(- 1)}^{2} + {(\frac{3}{2})}^{2} + {(- \frac{5}{2})}^{2}}$ m/s

role="math" localid="1653562766101" $= \sqrt{1 + \frac{9}{4} + \frac{25}{4}}$ m/s

$= \sqrt{\frac{4 + 9 + 25}{4}}$ m/s

= 3.08m/s

Thus, the magnitude of velocity vector is 3.08m/s .

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If $\vec{v} = <2, - 3, 5>$ m/s, then what is $|- \frac{1}{2} \vec{v}|$ ?

Short Answer

Step by step solution

Understanding the concept of multiplication of vector with a scalar

Determination of the velocity vector -12v→

Determination of magnitude of -12v→

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If v→=2,-3,5m/s, then what is-12v→ ?

Short Answer

Step by step solution

Understanding the concept of multiplication of vector with a scalar

Determination of the velocity vector -12v→

Determination of magnitude of -12v→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Electric Charge Field and Potential

Oscillations

Astrophysics

Atoms and Radioactivity

Translational Dynamics

Study anywhere. Anytime. Across all devices.

If $\vec{v} = <2, - 3, 5>$ m/s, then what is $|- \frac{1}{2} \vec{v}|$ ?