Question

What is the $\mathit{y}$component of the vector $\mathbf{(}\mathbf{3}\stackrel{\mathbf{\wedge }}{\mathbf{i}}\mathbf{-}\mathbf{8}\stackrel{\mathbf{\wedge }}{\mathbf{k}}\mathbf{)}\mathbf{m}\mathbf{/}\mathbf{s}$?

(a)$\mathbf{3}\mathbf{m}\mathbf{/}\mathbf{s}$

(b) $\mathbf{-}\mathbf{8}\mathbf{m}\mathbf{/}\mathbf{s}$

(c)$\mathbf{0}$

(d)8 m/s

(e) none of those answers

Short answer

The correct option is (c) 0 m/s.

Step-by-step solution

Define the vector

A quantity that has both magnitude and direction is called a vector.

It's usually represented by an arrow with the same direction as the amount and a length proportionate to the magnitude of the quantity.

Determining  the y component of the given vector

When a vector is conceptualised,$\overrightarrow{A}$is of the form$\overrightarrow{A}=A_x\hat{i}+A_y\hat{j}+A_z\hat{k},$here$A_x$is x-component of$\overrightarrow{A},$$A_y$is y component of$\overrightarrow{A}$and$A_z$is the z-component of$\overrightarrow{A}$

Analyze the vector that has been given in the question$(3\stackrel{\wedge }{\mathrm{i}}-8\stackrel{\wedge }{\mathrm{k}})\mathrm{m}/\mathrm{s}$.Compare this vector with$\overrightarrow{A}=A_x\hat{i}+A_y\hat{j}+A_z\hat{k}$

x-component of the given vector is 3 m/s.

y-component of the given vector is 0.

z-component of the given vector is -8 m/s.

Thus the option (c) is correct

Explanation for option (a)

Since the y-component of the given vector is 0.

Thus the option (a) is incorrect.

Explanation for option (b)

Since the y-component of the given vector is 0.

Thus the option (b) is incorrect

Explanation for option (d)

Since the y-component of the given vector is 0.

Thus the option (d) is incorrect.