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To a man running upwards on a hill, the ...

To a man running upwards on a hill, the rain appears to fall vertically downwards with `4ms^(-1)` . The velocity vector of the man with respect to earth is `2 hati +3hat j` . If the man starts running down the hill with the same speed, then what will be the relative speed of the rain with respect to man?

Text Solution

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`vecv_(R.M) = vecv_(R.G) - vecv_(M.G)`
` - 4 hatj = vecv_(R.G) - ( 2hati + 3hatj)`
` vecv_(R.G) = + 2hati -hatj`
When man starts running down ` v_(M.G) = - ( 2hati + 3hatj)`
` vecv_(R.M) = vecV_(R.G) - vec_(M.G) = ( 2hati - hatj) + 2hati + 3hatj = 4hati + 2hatj`
Speed ` |vecV_(R.M)| = sqrt(16+4) = sqrt20 ` m/s
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