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A boat is moving with a velocity v(bw)=5...

A boat is moving with a velocity `v_(bw)=5 km//hr` relative to water. At time `t=0`.the boat passes through a piece of cork floating in water while moving down stream.If it turns back at time `t_(1)=30 min`.
a) when the boat meet the cork again?
b) The distance travelled by the boat during this time.

Text Solution

Verified by Experts

Time of travelling of both from A to B ,`(T_(1))` and B to C , `(T'_(1)=`time of moving the cork from `A` to `C`.
.
Velocity of boat from `A` to `B`
`vec v_(b,w)+vedc v_(w)=(5+u)km h^(-1)`
And velocity of boat from `B` to `C`
`vec v_(b,w)+vedc v_(w)=(5+u)km h^(-1)`
Distance moved by boat in time `t'_(1)`
`AB=(5+4)t_(1)`
And disannce moved by boat in time`t'_(1)=BC=(5-u)t'_(1)`
Distance moved by cord during this time
`AC=u(t_(1)+t'_(1))`
But `AB=AC+BC`
`(5+u)t_(1)=u(t_(1)+t'_(1))+(5-u)t'_(1)`
`5t_(1)=5t'_(1) rArr t'_(1)=t_(1)=30 min`
Hence, the cord meets the boat again aftre ` 1 h`.`
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