csat-suneung 2006 Q29

csat-suneung · South-Korea · csat__math-science 4 marks Connected Rates of Change Geometric Related Rates with Distance or Angle
The distance between point O and point E is 40 m. As shown in the figure on the right, person A departs from point O and runs along the half-line OS perpendicular to segment OE at a constant speed of 3 m/s, and person B departs from point E 10 seconds after person A starts and runs along the half-line EN perpendicular to segment OE at a constant speed of 4 m/s. The angle formed by the intersection of the segment connecting the positions of persons A and B with segment OE is $\theta$ (in radians). What is the rate of change of $\theta$ at the moment 20 seconds after person A departs? [4 points]
(1) $\frac { 21 } { 290 }$ radians/second
(2) $\frac { 13 } { 290 }$ radians/second
(3) $\frac { 7 } { 290 }$ radians/second
(4) $\frac { 3 } { 290 }$ radians/second
(5) $\frac { 1 } { 290 }$ radians/second
The distance between point O and point E is 40 m. As shown in the figure on the right, person A departs from point O and runs along the half-line OS perpendicular to segment OE at a constant speed of 3 m/s, and person B departs from point E 10 seconds after person A starts and runs along the half-line EN perpendicular to segment OE at a constant speed of 4 m/s. The angle formed by the intersection of the segment connecting the positions of persons A and B with segment OE is $\theta$ (in radians). What is the rate of change of $\theta$ at the moment 20 seconds after person A departs? [4 points]\\
(1) $\frac { 21 } { 290 }$ radians/second\\
(2) $\frac { 13 } { 290 }$ radians/second\\
(3) $\frac { 7 } { 290 }$ radians/second\\
(4) $\frac { 3 } { 290 }$ radians/second\\
(5) $\frac { 1 } { 290 }$ radians/second