Final answer:
To calculate how long the collision lasted, we used the impulse-momentum theorem. The change in momentum is the mass multiplied by the difference in velocities. Dividing the change in momentum by the force gives us the duration of the collision which is 0.225 seconds.
Step-by-step explanation:
To determine how long the collision between the soccer ball and defender lasted, we can use the impulse-momentum theorem which states that the impulse applied to an object is equal to the change in momentum of the object. Here, the change in momentum (Δp) can be calculated by finding the difference between the final and initial momentum. The formula for momentum (p) is mass (m) times velocity (v), so Δp = m × v_final - m × v_initial.
Given a soccer ball mass of 2.1 kg, initial velocity of 9 m/s, final velocity of 15 m/s, and force applied of 56 N, we can calculate:
Δp = (2.1 kg) × (15 m/s) - (2.1 kg) × (9 m/s) = 31.5 kg·m/s - 18.9 kg·m/s = 12.6 kg·m/s.
The impulse (J) can also be expressed as the force (F) multiplied by the time (t) during which the force is applied, J = F × t.
Using the force of 56 N, we can express the time as t = J / F. Substituting the values, t = (12.6 kg·m/s) / (56 N).
Performing the calculation gives us: t = 0.225 seconds. Therefore, the collision lasted for 0.225 seconds.