Question

An object is moving with velocity $10\text{m/s}$ as shown in figure. Determine the speed of image with respect to ground.

• A. $8\hat{i}+6\hat{j}$
• B. $-8\hat{i}-6\hat{j}$
• C. $-8\hat{i}+6\hat{j}$
• D. None

Answer 1

The correct option is C $-8\hat{i}+6\hat{j}$

Given:
$v=10\text{m/s};\theta ={37}^{\circ }$


Components of the velocity of object along $x\text{and}y$ axis are

$V_{Ox}=10\cos {37}^{\circ }=10\times \frac{4}{5}=8\hat{i}\text{m/s}$

$V_{Oy}=10\sin {37}^{\circ }=10\times \frac{3}{5}=6\hat{j}\text{m/s}$

As we know that velocity of image along $x-$axis is,

$V_{Ix}=-V_{Ox}=-8\hat{i}\text{m/s}$, and

Velocity of image along $y-$axis is,

$V_{Iy}=V_{Oy}=6\hat{j}\text{m/s}$

Now, the total velocity of image,

$V_I=V_{Ix}\hat{i}+V_{Oy}\hat{j}=-8\hat{i}+6\hat{j}\text{m/s}$

Hence, option (a) is correct answer.