The human head can be considered as a 3.3-kg cranium protecting a 1.5-kg brain, with a small amount of cerebrospinal fluid that allows the brain to move a little bit inside the cranium. Suppose a cranium at rest is subjected to a force of 2800 N for 6.5 ms in the forward direction.

(a) What is the final speed of the cranium?

(b) The back of the cranium then collides with the back of the brain, which is still at rest, and the two move together. What is their final speed?

(c) The cranium now hits an external object and suddenly comes to rest, but the brain continues to move forward. If the front of the brain interacts with the front of the cranium over a period of 15 ms before coming to rest, what average force is exerted on the brain by the cranium?