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a man travelling southward at 15km/h observes that the wind appears to be coming from west on incresing his speed to 25km/h it appears to be coming from southwest.find direction and speed of the wind

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Questioner:ghazal
Country:Sindh, Pakistan
Category:Advanced Math
Private:Yes   <<<<<<<<<<<<<<<<< changed
Subject:physics
Question:

a man travelling southward at 15km/h observes that the wind appears to be coming from west on incresing his speed to 25km/h it appears to be coming from southwest.find direction and speed of the wind
.............................................................

Let's assign:

<x, y> = the vector velocity of the wind.

travelling southward at 15km/h -->  <0,-15>

Then  <0,-15> + <x, y> is the apparent V.V. of the wind = <x, y - 15>

But he thinks the wind is coming from the west (i.e. going due east), so
he thinks  y - 15 = 0, or y = 15

...............

travelling southward at 25km/h -->  <0,-25>

Then  <0,-25> + <x, y> is the apparent V.V. of the wind = <x, y - 25>

But he thinks the wind is coming from the southwest (i.e. going due northeast), so he thinks  y - 25 = x.

Since y = 15,  x = 15 - 25 = -10

......................
So the V.V. of the wind = <-10,15>.  You can finish up.

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