Calculate the Distance Fred and Brutus Slide After Collision

How far do Fred and Brutus slide after their collision?

A. Approximately 1.45 meters

Answer:

They slide a distance of approximately 1.45 meters.

When Fred (mass 63kg) and Brutus (mass 130kg) collide while running, they slide a distance of approximately 1.45 meters after falling to the ground. This distance is influenced by the coefficient of kinetic friction between their football uniforms and the Astroturf surface. To calculate this distance accurately, we need to consider the forces acting on the system and apply Newton's laws of motion.

The key force to consider in this scenario is the force of kinetic friction between the players and the ground. The force of kinetic friction (Kf) can be calculated using the equation: Kf = μk * N, where μk is the coefficient of kinetic friction and N is the normal force.

The normal force can be calculated as the sum of the individual weights of Fred and Brutus: N = mg1 + mg2. By determining the net force acting on the system, we can equate the force of kinetic friction to the net force: Fnet = Kf.

Since they are moving at a constant speed, the acceleration is zero, resulting in the net force being zero as well. By setting Kf = Fnet and substituting the values, we can calculate the acceleration (a) using the formula: a = (μk * N) / (m1 + m2).

Finally, by applying the equation of motion to calculate the distance (d) they slide: d = v^2 / (2a). Substituting the given values and calculating the normal force (N) and acceleration (a), we find that they slide a distance of approximately 1.45 meters when they collide and fall to the ground.

The coefficient of kinetic friction between their football uniforms and Astroturf plays a crucial role in determining the distance they slide after the collision.