91Ó°ÊÓ

A rocket engine can accelerate a rocket launched from rest vertically up with an acceleration of \(20.0 \mathrm{m} / \mathrm{s}^{2}\) However, after 50.0 s of flight the engine fails. (a) What is the rocket's altitude when the engine fails? (b) When does it reach its maximum height? (c) What is the maximum height reached? [Hint: A graphical solution may be easiest.] \((\mathrm{d})\) What is the velocity of the rocket just before it hits the ground?

Find the point of no return for an airport runway of \(1.50 \mathrm{mi}\) in length if a jet plane can accelerate at \(10.0 \mathrm{ft} / \mathrm{s}^{2}\) and decelerate at \(7.00 \mathrm{ft} / \mathrm{s}^{2} .\) The point of no return occurs when the pilot can no longer abort the takeoff without running out of runway. What length of time is available from the start of the motion in which to decide on a course of action?

In the human nervous system, signals are transmitted along neurons as action potentials that travel at speeds of up to \(100 \mathrm{m} / \mathrm{s} .\) (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 1.0 -m-long sensory neuron to the spinal column, across a synapse to a second 1.0 -m-long neuron, and across a second synapse to the brain. Suppose that the synapses are each \(100 \mathrm{nm}\) wide, that it takes \(0.10 \mathrm{ms}\) for the signal to cross each synapse, and that the action potentials travel at \(100 \mathrm{m} / \mathrm{s} .\) (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?