A propeller is rotating about an axis perpendicular to its center, as the drawin

Question

A propeller is rotating about an axis perpendicular to its center, as the drawing shows. The axis is parallel to the ground. An arrow is fired at the propeller, travels parallel to the axis, and passes through one of the open spaces between the propeller blades. The angular open spaces between the three propeller blades are each ?/3 rad (60.0?). The vertical drop of the arrow may be ignored. What is a maximum value ? for the angular speed of the propeller, beyond which the arrow cannot pass through an open space without being struck by one of the blades. Find this maximum value when the arrow has length L and speed v shown in the following table. The numbers in the table are: L v (a) 0.75 m 71.3 m/s (b) 0.75 m 95.3 m/s (c) 0.94 m 95.3 m/s http://edugen.wileyplus.com/edugen/courses/crs6407/art/qb/qu/c08/EAT_1320551660832_0_5445114283181287.gif Here is the picture as well, hope it helps!!!

Explanation / Answer

the angular opening thru which arrow must fly = /3
{3 prop blades x /3 = rad is closed & /3 rad angluar space between is open}

The times of flight of arrow are:
(a) 0.64/75 = 0.00842 s
(b) 0.64/90 = 0.00711 s
(c) 0.84/90 = 0.00933 s

The angular speeds just letting arrow thru are:
(a) /3/0.00843 = 124 rad/s ANS
(b) /3/0.00711 = 147 rad/s ANS
(c) /3/0.00933 = 112 rad/s ANS

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