Q23P If is B鈬赌added to C鈬赌=3.0聽i+4... [FREE SOLUTION]

Chapter 3: Q23P (page 58)

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

Short Answer

Expert verified

Magnitude of $\overset{鈬赌}{B} = 3.2$

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.

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

Thus the magnitude is given by

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

Given are

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

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

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

To find magnitude of vector C⇀

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

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

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

To find magnitude of vector B⇀

As the resultant in the positive y direction

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

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91影视

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

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.

Most popular questions from this chapter

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91影视

If is B鈬赌added to C鈬赌=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鈬赌. What is the magnitude ofB鈬赌?

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

Atoms and Radioactivity

Electric Charge Field and Potential

Rotational Dynamics

Waves Physics

Space Physics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

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