Question 116: Motion in 2D & Vectors

Question

The $x, y$ components of vector $\mathbf{P}$ have magnitudes 1 and 3 and $x, y$ components of resultant of $\mathbf{P}$ and $\mathbf{Q}$ have magnitudes 5 and 6, respectively. What is the magnitude of $\mathbf{Q}$ ?

Accepted Answer

Given :
$\mathbf{P} = \hat{\mathbf{i}} + 3 \hat{\mathbf{j}}$
Resultant :
$\mathbf{R} = 5 \hat{\mathbf{i}} + 6 \hat{\mathbf{j}} = \mathbf{P} + \mathbf{Q}$
Let's find the components of vector $\mathbf{Q}$ :
$ \Rightarrow \mathbf{Q} = \mathbf{R} - \mathbf{P} $
$ \mathbf{Q} = (5 \hat{\mathbf{i}} + 6 \hat{\mathbf{j}}) - (\hat{\mathbf{i}} + 3 \hat{\mathbf{j}}) $
$ \mathbf{Q} = 4 \hat{\mathbf{i}} + 3 \hat{\mathbf{j}} $
To find the magnitude of $\mathbf{Q}$ :
$ |\mathbf{Q}| = \sqrt{(4)^2 + (3)^2} $
$ |\mathbf{Q}| = \sqrt{16 + 9} $
$ |\mathbf{Q}| = \sqrt{25} $
$ |\mathbf{Q}| = 5 	ext{ units} $

Answer

5

Answer

4

Answer

3

Answer

2

Motion in 2D & Vectors

The x, y components of vector \mathbf{P} have magnitudes 1 and 3 and x, y components of resultant of \mathbf{P} and \mathbf{Q} have magnitudes 5 and 6, respectively. What is the magnitude of \mathbf{Q} ?

Choose the correct answer: