Question

A cricket ball of mass $150g$ has an initial velocity $u=3\hat{i}+4jm/s$ and a final velocity $v=-(3\hat{i}+4j)m/s$ after being hit. The change in momentum (final momentum-initial momentum) is (in kg m/s)

• A. $-(0.45\hat{i}+0.6\hat{j})$
• B. zero
• C. $–5(\hat{i}+\hat{j})$
• D. $–(0.9\hat{i}+1.2\hat{j})$

Answer 1

The correct option is D $–(0.9\hat{i}+1.2\hat{j})$

Step 1: Find initial momentum.

Formula used: $\left(\overrightarrow{p}\right)=m\overrightarrow{u}$

Given,

Mass $=150g=.15kg$

$\overrightarrow{u}=3\hat{i}+4\hat{j}m/s$

Initial momentum, $\left(\overrightarrow{p}\right)=m\overrightarrow{u}$

$=\left(0.15kg\right)3\hat{i}+4\hat{j}m/s$

$=0.45\hat{i}+0.6\hat{j}kgm/s$

Step 2: Find final momentum.

Formula use: $\left(\overrightarrow{p}\right)=m\overrightarrow{v}$

As given that $v=-(3\hat{i}+4\hat{j})m/s$

Final momentum, $\left(\overrightarrow{p}\right)=m\overrightarrow{v}$

$=\left(0.15kg\right)(-3\hat{i}-4\hat{j}m/s)$

$=(-0.45\hat{i}-0.6\hat{j})kgm/s$

Step 3: Find change in momentum.
change in momentum, $△\overrightarrow{p}={\overrightarrow{p_f}}_{}-\overrightarrow{p_i}$​

$=(-0.45\hat{i}-0.6\hat{j})-(0.45\hat{i}+0.6\hat{j})$

$=-(0.9\hat{i}+1.2\hat{j})kgm/s$