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A man is running up an incline planr maaking an angle $\theta$ with horizontal with a speed u .Rain drops falling at an angle $\alpha$ with the vertical appear to the man as if they are falling at an angle of $45^o$ with the horizontal. The speed of rain drops is

#Mechanics #Hctib

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Take relative velocity along x and y axes and equate magnitude

Raghav Vaidyanathan - 5 years, 6 months ago

While talking about the rain, you took its direction in the south west direction. What prompted you to do that?? Why didn't you take it in the south-east direction?? In that case the x-component of relative velocity will be

ucos(theta)-vsin(alpha) and not ucos(theta)+vsin(alpha) as in this case...

Abhineet Nayyar - 5 years, 6 months ago

Both are equivalent. Just interchange $\alpha$ in my equation with $-\alpha$ to get to the result that you have mentioned. This disparity arises since I am measuring the angle in the clockwise direction, while you are measuring it in the anticlockwise direction.

Raghav Vaidyanathan - 5 years, 6 months ago

@Raghav Vaidyanathan – Yea, but the final expressions for the velocity are completely different...Then how are the results equivalent??

Abhineet Nayyar - 5 years, 6 months ago

@Raghav Vaidyanathan @Tanishq Varshney @Ronak Agarwal

Kyle Finch - 5 years, 6 months ago

$v=u \sin {(\pi/4 -\theta)} \csc {(\pi/4 -\alpha)}$

Raghav Vaidyanathan - 5 years, 6 months ago

Can u explain in brief

Kyle Finch - 5 years, 6 months ago

Shouldn't be there plus sign in sin part

Kyle Finch - 5 years, 6 months ago

Yes i solved it . Any way thanx for helping .

Kyle Finch - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$