3. a 2 kg ball hits a surface with a speed of 5 m/s and bounces back with a speed of 2.5 m/s. determine the…

Explanation:

Step1: Recall momentum formula

Momentum ( p = mv ), where ( m ) is mass and ( v ) is velocity. Momentum change ( \Delta p = p_f - p_i ).

Step2: Define initial and final velocities

Let initial velocity ( v_i = 5 , \text{m/s} ) (towards the surface, positive direction), final velocity ( v_f = -2.5 , \text{m/s} ) (bounces back, negative direction). Mass ( m = 2 , \text{kg} ).

Step3: Calculate initial momentum

( p_i = m v_i = 2 \times 5 = 10 , \text{kg·m/s} )

Step4: Calculate final momentum

( p_f = m v_f = 2 \times (-2.5) = -5 , \text{kg·m/s} )

Step5: Calculate momentum change

( \Delta p = p_f - p_i = -5 - 10 = -15 , \text{kg·m/s} ). The negative sign indicates direction, magnitude of change is ( 15 , \text{kg·m/s} ).

Answer:

The momentum change of the ball is (\boldsymbol{-15 , \text{kg·m/s}}) (or a magnitude of (15 , \text{kg·m/s}) in the direction opposite to the initial velocity).