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Chapter 12: Problem 200
Determine the constant speed at which the cable at \(A\) must be drawn in by the motor in order to hoist the load \(6 \mathrm{~m}\) in \(1.5 \mathrm{~s}\).
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The girl at \(A\) can throw a ball at \(v_{A}=10 \mathrm{~m} / \mathrm{s}\) Calculate the maximum possible range \(R=R_{\max }\) and the associated angle \(\theta\) at which it should be thrown. Assume the ball is caught at \(B\) at the same elevation from which it is thrown.
The double collar \(C\) is pin connected together such that one collar slides over the fixed rod and the other slides over the rotating \(\operatorname{rod} A B .\) If the angular velocity of \(A B\) is given as \(\dot{\theta}=\left(e^{n .5^{2}}\right) \mathrm{rad} / \mathrm{s}\), where \(t\) is in seconds, and the path defined by the fixed rod is \(r=|(0.4 \sin \theta+0.2)| \mathrm{m}\), determine the radial and transverse components of the collar's velocity and acceleration when \(t=1 \mathrm{~s}\). When \(t=0, \theta=0 .\) Use Simpson's rule with \(n=50\) to determine \(\theta\) at \(t=1 \mathrm{~s}\).
A particle moves along a path defined by polar coordinates \(r=\left(2 e^{t}\right) \mathrm{ft}\) and \(\theta=\left(8 t^{2}\right)\) rad, where \(t\) is in seconds. Determine the components of its velocity and acceleration when \(t=1 \mathrm{~s}\).
Two cars start from rest side by side and travel along a straight road. Car \(A\) accelerates at \(4 \mathrm{~m} / \mathrm{s}^{2}\) for \(10 \mathrm{~s}\) and then maintains a constant speed. Car \(B\) accelerates at \(5 \mathrm{~m} / \mathrm{s}^{2}\) until reaching a constant speed of \(25 \mathrm{~m} / \mathrm{s}\) and then maintains this speed. Construct the \(a-t, v-t\), and \(s-t\) graphs for each car until \(t=15 \mathrm{~s}\). What is the distance between the two cars when \(t=15 \mathrm{~s}\) ?
A horse on the merry-go-round moves according to the equations \(r=8 \mathrm{ft}, \theta=(0.6 t) \mathrm{rad}\), and \(z=(1.5 \sin \theta) \mathrm{ft}\), where \(t\) is in seconds. Determine the cylindrical components of the velocity and acceleration of the horse when \(t=4 \mathrm{~s}\).
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