A ball of mass 800g moving horizontally with a speed of 5m/s hits a vertical wall and rebounds with the same speed. The impulse experienced by the ball is?

Analyze the question: A ball hits a wall and rebounds at the same speed. We need the impulse, which equals the change in momentum.

Concept: Impulse = change in momentum = m(v − u)

Momentum is a vector, so direction matters. If the ball's initial direction is taken as positive, the rebound velocity is negative.

Solution:

• Mass: m = 800 g = 0.8 kg
• Initial velocity: u = +5 m/s
• Final velocity: v = −5 m/s (same speed, opposite direction)

Impulse = m(v − u) = 0.8 × (−5 − 5) = 0.8 × (−10) = −8 kg m/s

The magnitude is 8 kg m/s. The negative sign only shows that the impulse acts opposite to the ball's original direction of motion (the wall pushes the ball back).

Checking the other options:

• A (0): this would be wrong, because it treats the momentum as unchanged. Speed is unchanged, but velocity is not, since the direction reverses.
• B (2) and C (4): these come from mistakes such as forgetting to convert grams to kg or forgetting the reversal (4 kg m/s is just the momentum before impact: 0.8 × 5).

Answer: The impulse has a magnitude of 8 kg m/s, which is option D.

Exam tip: When a ball bounces back with the same speed, the change in velocity is 2v, not zero. So impulse = 2mv. Always convert grams to kilograms first, and remember that if the ball stops instead of rebounding, the impulse would be only mv.