{"id":11565,"date":"2022-07-18T15:00:35","date_gmt":"2022-07-18T09:30:35","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11565"},"modified":"2022-07-18T15:00:39","modified_gmt":"2022-07-18T09:30:39","slug":"nazima-is-fly-fishing-in-a-stream-the-tip-of-her-fishing-rod-is-1-8-m-above-the-surface-of-the-water-and-the-fly-at-the-end-of-the-string-rests-on-the-water-3-6-m-away-and-2-4-m-from-a-point-directly","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/nazima-is-fly-fishing-in-a-stream-the-tip-of-her-fishing-rod-is-1-8-m-above-the-surface-of-the-water-and-the-fly-at-the-end-of-the-string-rests-on-the-water-3-6-m-away-and-2-4-m-from-a-point-directly\/","title":{"rendered":"Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string ( from the tip of her rod to the fly) is taut, how much string does she have out (see fig.) ? If she pulls in the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds ?"},"content":{"rendered":"
Let O be the position of nazima at the time of fishing.<\/p>\n
Let OA be the rod and AB be the string.<\/p>\n
Height of the tip of rod above sea level.<\/p>\n
i.e.\u00a0 \u00a0 AC = 1.8 m<\/p>\n
The distance of the fly from the girl = 3.6 m<\/p>\n
i.e.\u00a0 \u00a0OB = 3.6 m<\/p>\n
In triangle ABC,<\/p>\n
\\({AB}^2\\) = \\({CB}^2\\) + \\({AC}^2\\) = \\((3.6 – 1.2)^2\\) + \\((1.5)^2\\)<\/p>\n
= 5.76 + 3.24 = 9 m<\/p>\n
\\(\\implies\\)\u00a0 \u00a0AB = 3 m<\/p>\n
The rate of pulling the string = 5 cm\/sec.<\/p>\n
In 12 sec, the girl will pull = 12 \\(\\times\\) 5 = 60 cm<\/p>\n
The remaining length of the string AD = 3 – 0.6 = 2.4 m<\/p>\n
New position of the string is AD.<\/p>\n
In right triangle ACD,<\/p>\n
\\({CD}^2\\) = \\({AD}^2\\) – \\({AC}^2\\)<\/p>\n
= 5.76 – 3.24 = 2.52<\/p>\n
CD = 1.6 m<\/p>\n
OD = distance of the fly from her<\/p>\n
\\(\\implies\\)\u00a0 OD = OC + CD = 1.2 + 1.6 = 2.8 m<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Solution : Let O be the position of nazima at the time of fishing. Let OA be the rod and AB be the string. Height of the tip of rod above sea level. i.e.\u00a0 \u00a0 AC = 1.8 m The distance of the fly from the girl = 3.6 m i.e.\u00a0 \u00a0OB = 3.6 m …<\/p>\n