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Rain is falling with a velocity (-4hat(i...

Rain is falling with a velocity `(-4hat(i)+8hat(j)-10hat(k))`. A person is moving with a velocity of `(6hat(i)+8hat(j))` on the ground.
The speed with the rain drops hit the person is `:`

A

`10m//s`

B

`10sqrt(2)m//s`

C

`sqrt(180)m//s`

D

`sqrt(360)m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(V)_(rm)=vec(V)_(r)-vec(V)_(m)=(-10hat(i)-10hat(k))`
Ans. `(-10hat(i)-10hat(k))` rain appears to come `45^(@)` with `hat (j)`
`V_(m)=sqrt(10^(2)+10^(2))=10sqrt(2)m //sec.`
`W_(CL)|_("accelerated motion") =DeltaKE-W_("friction")` where `W_(CL)` is work down by camel on load.
`=[(1)/(2)mv^(2)-0]-[-mu_(kk) mg . 50]=1000[(125)/(2)]`
similarly, `W_(CL)|_("acceleration")=DeltaKE-W_(f r iction)[0-(1)/(2)mv^(2)]-[-mu_(k)mg.50]=100[(75)/(2)]`
`:. (W_(CL)|_("acceleration motion"))/(W_(CL)|_("retarded motion"))`
`=(125)/(75)=(5)/(3)`
`rArr 5:3`
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