In the human nervous system, signals are transmitted along neurons as "action potentials" that travel at speeds of up to 100 m/s. (An action potential is a traveling influx of sodium ions through the membrane of a neuron.) The signal is passed from one neuron to another by the release of neurotransmitters in the synapse. Suppose someone steps on your toe. The pain signal travels along a 1.2 m long sensory neuron to the spinal column, across a synapse to a second 1.2 m long neuron, and across a second synapse to the brain. Suppose that the synapses are each 98 nm wide; that it takes 0.09 ms for the signal to cross each synapse; and that the action potentials travel at 94 m/s.
(a) At what average speed does the signal cross a synapse?
(b) How long does it take the signal to reach the brain?
(c) What is the average speed of propagation of the signal?