Question

Sassbot and Block Ness Monster play roller derby for the Reservoir Dolls, a roller derby team in Madison, Wisconsin. In a particular bout against the Unholy Rollers, another Madison team, Sassbot is playing the position of jammer: she must pass members of the Unholy Rollers in order to score points. Block Ness Monster is playing as a blocker: she must help Sassbot while also stopping the Unholy Rollers’ jammer. During a crucial moment in the bout, Monster sees that Sass, a few feet in front of her, is about to get hit by Skullz B. Kraken, a member of the Unholy Rollers. Monster reaches Sass quickly and pushes her forward, attempting to give Sass a boost of speed so she is out of the Skullz’s reach. Monster pushes Sass straight forward, delivering the push at Sass’s center of mass, her lower back, so that Sass does not experience any rotation due to the push. Neither Monster nor Sass are using their wheels to brake immediately before, during, or after the push, so the outside forces on them are negligible. Monster’s mass is 82 kg. Sass’s mass is 55 kg. Monster’s speed before the push is 2 m·s−1, and Sass’s speed before the push is 0.75 m·s−1. Monster and Sass have found, in previous practice, that the average coefficient of restitution of this sort of push between them is 0.8. The coefficient of restitution is defined as the ratio of the difference in two objects’ velocities after the collision to that of the difference in the objects’ velocities before the collision. e = v2,f − v1,fv2,i − v1,i At the moment Monster finishes her push, Skullz is 0.75 m to the left and 1.1 m in front of Sass. Skullz is moving laterally (to the right) at a speed of 2.15 m·s−1 in her attempt to hit Sass. Sass is moving directly forward after Monster’s push. Will Sass get hit by Skullz or will she get past her in time?

How long will it take Sass to travel forward past Skullz’s position?

Answer 1

Let's consider that the people involved are behaving as particles. Using the conservation of momentum for Saas and Monster:

And using the concept of coeffient of restitution:

We have 2 equations with two unkonws. Then:

After pushing, Sass is moving forward with a speed of 2.0967 m/s. For they to collide, Sass should move at a speed of:

But since she moves with a lower velocity, Skullz pass to the collision point before Sass, so they don't collide.

Another way to check about collision is to suposse that the time of both Sass and Skullz to get the collision point is the same. Then:

Which indicates that Skullz will get to the collision point before Sass (Skullz is traveling faster than needed to hit Sass). They get to the collision point with a difference in time of 0.1758 s. If we consider them as particles (as stated before), they don't collide. But, how much distance do they travel in this difference in time?

If we consider real dimensions of bodies, it is possible that Skullz can "hit" Sass with "extended arms" due to there is a difference in distances of about 30cm.