Force of a foot When an individual is walking, the magnitude F of the vertical force of on...

Force of a foot When an individual is walking, the magnitude F of the vertical force of one foot on the ground (see the figure) can be described by

where t is time in seconds, A >0, b >0, and 0 < a < 1.

EXERCISE

(a) Show that F = 0 when t = −π/(2b) and t = π/(2b). (The time t = −π/(2b) corresponds to the moment when the foot first touches the ground and the weight of the body is being supported by the other foot.)

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(b) The maximum force occurs when

If , find the solutions of this equation for the interval −π/(2b) < t<π/(2b).

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(c) If , express the maximum force in terms of A.