Another trig/physics problem?
I can't find anything in the book on this or online please explain , I have a midterm wed on this stuff.
A 2600lb car traveling uphill had a grade resistance of 140pounds. Use a tangent function to estimate the angle of the grade?
The answer is 3.1
A wheel rotating at 8 radian/sec, and the wheel has a 47 inch diameter. What is the velocity of a point on the rim in ft/min?
The answer is 940 ft/min.
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Verified answer
1.) The grade resistance is just the component of the weight in the direction
of the grade. In this case we are given masses, but the formula will be the
same; with theta being the grade angle, we have tan(theta) = 140/2600 ---->
theta = arctan(140/2600) = 3.1 degrees to 1 decimal place.
2.) Velocity v = r*w where r is the radius and w is the angular speed. In this case
r = (47/2) inches = (47/24) feet and w = 8 rad/s * (60 s/min) = 480 rad/min.
Thus v = (47/24)*(480) = 47*20 = 940 ft/min
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