The frequency F of a fire truck siren heard by a stationary observer is given be

Question

The frequency F of a fire truck siren heard by a stationary observer is given below, where plusminus v represents the velocity of the accelerating fire truck in meters per second (see figure). (Round your answers to 3 decimal places.) F = 131, 300/340 plusminus v Find the rate of change of F with respect to v when the fire truck is approaching at a velocity of 29 meters per second (use -v). Find the rate of change of F with respect to v when the fire truck is moving away at a velocity of 29 meters per second (use +v). A 25-centimeter pendulum moves according to the equation theta = 0.15 sin (7t), where theta is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement theta_max and the rate of change of theta when t = 4 seconds. (Round your answers to three decimal places.)

Explanation / Answer

Solution(19)

sin is a PERIODIC function.

its value varies between -1 and +1. its max value is +1,

so the max displacement is 0.15(1) = 0.15

And rate of change of theta is;

d(theta)/dt = d/dt (0.15sin(7t)) = 0.15(7 cos(7t)) = 1.05 cos(7t)

At t = 4;

d(theta)/dt = 1.05 cos(7*4) = -1.0107 rad/s

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