Ethernet uses Carrier Sense Multiple Access with Collision Detection $($CSMA$/$CD$)$ for its media access control. Thus, each node listens while transmitting a frame to detect when a frame collided with another frame transmitted by another node. However, if a frame is too short, a node sometimes cannot detect a collision.

a$.$ What can happen when a frame is too short?

b$.$ Assume a signal can propagate through a copper Ethernet wire at $1\mathrm{.}8*108$ m$/$s$.$ If the maximum distance between any two nodes is $900$ m and you use a $10-$Mbps Ethernet, what is the minimum frame size needed to detect collisions?

c$.$ If an Ethernet wire is made of a better material such that a signal can propagate through the wire at $2\mathrm{.}5*108$ m$/$s$,$ what is the new minimum frame size for your network?

d$.$ If the maximum distance between any two nodes increases to $1800$ m$,$ what is the new minimum frame size for your network using a copper Ethernet wire?

e$.$ Suppose you upgrade your network from a $10-$Mbps Ethernet to a $100-$Mbps Ethernet. How can you support this new $100-$Mbps Ethernet without changing the minimum frame size or moving the nodes?