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In Figure. , a plane mirror is moving wi...

In Figure. , a plane mirror is moving with a uniform speed of `5ms^(-1)` along negative x-direction and observer O is moving with a velocity of `10ms^(-1)`. What is the velocity of image of a particle P, moving with a velocity as shown in the figure, as observed by observer O? Also find its direction.

Text Solution

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Velocity of point P, `v_(p)=10(hati+hatj)`
Velocity of mirror `v_(m)=-5hati`
Velocity of partical relative to mirror is
`vecv_(p m) =-25hati+10hatj`
Velocity of image relative to observer
`vecv_(IO)=vecv_(p m)-vecv_(Om)=(-15hat(i)+10hat(j))-(vecv_(O)-vecv_(m))`
`=( -30hat(i) +10hat(j)) ms^(-1)`
Angle with X-axis,
`alpha= tan^(-1)(-1//3)`
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