Chapter 3: Q23P (page 58)

If is $\overset{⇀}{B}$ added to $\overset{⇀}{C} = 3.0 i + 4.0 \hat{j}$ , the result is a vector in the positive
direction of the y axis, with a magnitude equal to that of $\overset{⇀}{C}$ . What is the
magnitude of $\overset{⇀}{B}$ ?

Short Answer

Expert verified

Magnitude of $\overset{⇀}{B} = 3.2$

Step by step solution

To understand the concept

The resultant in this problem is in the positive y-direction so the x component will be zero and having magnitude equal to C. The magnitude of the unknown vector can be calculated using the law of addition which is explained by the following equation.

$\overset{⇀}{A} = x \hat{i} + y \hat{j}$

Thus the magnitude is given by

$|\overset{⇀}{A}| = \sqrt{x^{2} + y^{2}}$

Given are

$\overset{⇀}{B} + \overset{⇀}{C} = \overset{⇀}{R}$

Where $\overset{⇀}{R}$ is the resultant

$\overset{⇀}{C} = 3 \hat{i} + 4 \hat{j} |C| = |R|$

To find magnitude of vector C⇀

$\overset{⇀}{C} = 3 \hat{i} + 4 \hat{j}$

Using the equation (ii), magnitude of the vector $\overset{⇀}{C}$ can be written as

$|\overset{⇀}{C}| = \sqrt{3^{2} + 4^{2}} |\overset{⇀}{C}| = 5$

To find magnitude of vector B⇀

As the resultant in the positive y direction

$\overset{⇀}{R} = 5 \hat{j} \overset{⇀}{B} + \overset{⇀}{C} = \overset{⇀}{R} \overset{⇀}{B} + (3 \hat{i} + 4 \overset{⇀}{j}) = 5 \overset{⇀}{j} \overset{⇀}{B} = - 3 \hat{i} + \hat{j} |\overset{⇀}{B}| = \sqrt{- 3^{2} + 1^{2}} |\overset{⇀}{B}| = 3.2$

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If is $\overset{⇀}{B}$ added to $\overset{⇀}{C} = 3.0 i + 4.0 \hat{j}$ , the result is a vector in the positive
direction of the y axis, with a magnitude equal to that of $\overset{⇀}{C}$ . What is the
magnitude of $\overset{⇀}{B}$ ?

Short Answer

Step by step solution

To understand the concept

To find magnitude of vector C⇀

To find magnitude of vector B⇀

One App. One Place for Learning.

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If is B⇀added to C⇀=3.0i+4.0j^, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C⇀. What is the magnitude ofB⇀?

Short Answer

Step by step solution

To understand the concept

To find magnitude of vector C⇀

To find magnitude of vector B⇀

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Famous Physicists

Electricity and Magnetism

Fluids

Torque and Rotational Motion

Conservation of Energy and Momentum

Work Energy and Power

Study anywhere. Anytime. Across all devices.

If is $\overset{⇀}{B}$ added to $\overset{⇀}{C} = 3.0 i + 4.0 \hat{j}$ , the result is a vector in the positive
direction of the y axis, with a magnitude equal to that of $\overset{⇀}{C}$ . What is the
magnitude of $\overset{⇀}{B}$ ?