Question

A ball of mass m travelling with velocity 2i+3j receives an impulse -3mi. What is the velocity of ball
immediately afterwards ?​

Answer 1

Answer:

Velocity of the ball afterwards is $-\hat i+3\hat j$

Explanation:

Mass of the ball = m

Velocity of the ball = $2\hat i+3\hat j$

The ball receives an impulse of $-3m\hat i$

If the velocity of the ball afterwards is $\vec v$

Then, using

$\boxed{\text{Change in momentum}=\text{impulse recieved}}$

or, $\boxed{m(\vec v_f-\vec v_i)=J}$

or, $m[\vec v-(2\hat i+3\hat j)]=-3m\hat i$

$\implies \vec v-(2\hat i+3\hat j)=-3\hat i$

$\implies \vec v=-3\hat i+2\hat i+3\hat j$

$\implies \vec v=-\hat i+3\hat j$

Therefore, velocity of the ball afterwards is $-\hat i+3\hat j$