$\text { A petrol car is parked } 35 \text { feet from a long warehouse (see figure). The revolving }$

Multiple Choice

$\text { A petrol car is parked } 35 \text { feet from a long warehouse (see figure) . The revolving }$ light on top of the car turns at a rate of $\frac { 1 } { 2 }$ revolution per second. The rate at which the light beam moves along the wall is $r = 35 \pi \mathrm { sec } ^ { 2 } \theta \mathrm { ft } / \mathrm { sec }$ . Find the rate $r$ when $\theta$ is $\frac { \pi } { 6 }$ .

A) $r = \frac { 140 } { 3 } \mathrm { tt } / \mathrm { sec }$
B) $r = \frac { 70 \sqrt { 3 } \pi } { 3 } \mathrm { ft } / \mathrm { sec }$
C) $r = \frac { 70 \sqrt { 3 } } { 3 } \mathrm { ft } / \mathrm { sec }$
D) $r = \frac { 140 \pi } { 3 } \mathrm { ft } / \mathrm { sec }$
E) $r = \frac { 70 \pi } { 3 } \mathrm { ft } / \mathrm { sec }$