Impulse and velocity of a ball

Problem

Impulse and velocity. A $200\;\text{g}$ ball is struck by a racket. The average force is $50\;\text{N}$ applied for $4{,}0\;\text{ms}$. If the ball starts at rest, what is its final velocity?

Solution

Impulse (average force times time): $J = F\,\Delta t = 50\cdot 4{,}0\cdot 10^{-3} = 0{,}20\;\text{N}\cdot\text{s}$

Final velocity (impulse–momentum theorem, $J = m\,\Delta v$, with $m = 0{,}20\;\text{kg}$ and starting from rest): $v_f = \frac{J}{m} = \frac{0{,}20}{0{,}20} = 1{,}0\;\text{m/s}$

$\ev{J = 0{,}20\;\text{N}\cdot\text{s}, \quad v_f = 1{,}0\;\text{m/s}}$

Links

Topics: Momentum and collisions Concepts: Impulse · Momentum