Question

A soccer ball is dropped from a height of h₁ = 3.4 m above the ground. After it bounces, it only makes it to a height h₂= 2.45 m above the ground. The soccer ball has mass m=0.142 kg. What is the magnitude of the impulse, in kilogram meters per second, the soccer ball experienced during the bounce?

Answer 1

The magnitude of the impulse experienced by the soccer ball during the bounce is approximately 0.462 kg·m/s.

Step-by-step explanation:

The magnitude of the impulse experienced by the soccer ball during the bounce can be calculated using the equation:

Impulse = m * |v_f - v_i|

Where:

• m is the mass of the soccer ball (0.142 kg)
• v_f is the final velocity of the ball after the bounce
• v_i is the initial velocity of the ball before the bounce

Since the ball is dropped vertically from a height of 3.4 m, its initial velocity is zero. The final velocity can be determined using the equation:

v_f = √(2 * g * (h₂ - h₁))

Where:

• g is the acceleration due to gravity (approximately 9.8 m/s²)
• h₂ is the final height of the ball (2.45 m)
• h₁ is the initial height of the ball (3.4 m)

Plugging in the values, we find that the magnitude of the impulse experienced by the soccer ball during the bounce is approximately 0.462 kg·m/s.