Question

a batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 m per second if the mass of the ball is 0.15 kg determine impulse imparted to the ball(assume linear motion of the ball)

Answer 1

Impulse is change in momentum

Let the ball going in +x axis so it's velocity (v1) be 12m/s
Initial momentum= m×v1

When batsman hitted ball , he changed its direction but not magnitude(as per question) so,
velocity (v2) be$\red{ -12m/s}$

Final momentum=m×v2

$<b>$ Impulse=change in momentum
=>mv2-mv1
=>m(v2-v1)
=>0.15(-24)
=>3.6N in -ve x axis.

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

• Initial velocity (u) = 12 m/s
• final velocity (v) = -12 m/s
• mass (m) = 0.15 kg

Here final velocity is negative because batsmen hit the ball and it goes to the opposite direction but no change in magnitude.

Use formula for impulse

$\Large{\sf{\vec{I} \: = \: mv \: - \: mu}}$

⇒I = m(v - u)

⇒I = 0.15( -12 - 12)

⇒I = 0.15(-24)

⇒I = - 3.6 Ns

∴ Impulse is - 3.6 Ns

Here negative sign of Impulse denotes that it is along negative X - axis