CASE STUDY CHALLENGE
Application of Derivatives: Traffic Speed Detection
The traffic police has installed an Over Speed Violation Detection (OSVD) system at various locations. These cameras can capture speeding vehicles from a distance.
A camera is installed on a pole at a height of 5 m. It detects a car travelling away from the pole at a speed of 20 m/s. At any point, x m away from the base of the pole, the angle of elevation of the speed camera from the car C is θ.
On the basis of the above information, answer the following questions:
Answer the following:
| (i) | Express θ in terms of height of the camera installed on the pole and x. | [1] |
| (ii) | Find the value of dθ/dx. | [1] |
| (iii) |
(a) Find the rate of change of angle of elevation with respect to time at an instant when the car is 50 m away from the pole. — OR —
(b) If the rate of change of angle of elevation with respect to time of another car at a distance of 50 m from the base of the pole is 3/101 rad/s, then find the speed of the car. |
[2] |