A drone, is an aircraft without any human pilot and is controlled by a r...

Class 10 Maths Standard CBSE ADDITIONAL PRACTICE QUESTION 2023-24 Question no 38 case study based question Chapter 9 some applications of trigonometry

A drone, is an aircraft without any human pilot and is controlled by a remote control device. Its various applications include policing, surveillance, photography, precision agriculture, forest fire monitoring, river monitoring and so on. David used an advanced drone with high resolution camera during an expedition in a forest region which could fly upto 100 m height above the ground level. David rode on an open jeep to go deeper into the forest. The initial position of drone with respect to the open jeep on which David was riding is shown below. David’s jeep started moving to enter the forest at an average speed of 10 m/s. He Simultaneously started flying the drone in the same direction as that of the jeep. (i) David reached near one of the tallest trees in the forest. He stopped the drone at a horizontal distance of 5√3 m from the top of the tree and at a vertical distance of 65 m below its maximum vertical range. If the angle of elevation of the drone from the top of the tree was 30°, find the height of the tree. Show your work. 1 (ii) The drone was flying at a height of 30√3 metres at a constant speed in the horizontal direction when it spotted a zebra near a pond, right below the drone. The drone travelled for 30 metres from there and it could see the zebra, at the same place, at an angle of depression of θ from it. Draw a diagram to represent this situation and find θ. Show you work. 1 (iii) After 2 minutes of starting the expedition both the drone and the jeep stopped at the same moment so that the drone can capture some images. The position of the drone and the jeep when they stopped is as shown below. Find the average speed of the drone in m/s rounded off upto 2 decimal places. Show your work. OR (iii) At some point during the expedition, David kept the drone stationary for some time to capture the images of a tiger. The angle of depression from the drone to the tiger changed from 30° to 45° in 3 seconds as shown below. (Note: The figure is not to scale.) What was the average speed of the tiger during that time? Show your work. (Note: Take √3 as 1.73.)