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

Torque and Rotational Motion

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Measurements

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Electric Charge Field and Potential

Study anywhere. Anytime. Across all devices.

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