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An aircraft flies at 400 km//h in still ...

An aircraft flies at `400 km//h` in still air. A wind of `200sqrt2 km//h` is blowing from the south towards north. The pilot wishes to travel from A to a point B north east of A. Find the time of his journey if `AB=1000 km.`

A

`t=0.83h`

B

`t=1.83h`

C

`t=2.83h`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `v_w=200sqrt2 km//h`
`v_(aw)=400 km//h` and `v_a` should be along AB or in
north-east direction. Thus, the direction of `v_(aw)`
should be such as the resultant of `v_w` and `v_(aw)` is
along AB or in north-east direction.
Let `v_(aw)` makes an angle `alpha` with AB as shown in
fig. Applying sine law in triangle ABC, we
get
`(CB)/ sin45^@=(AC)/sin alpha`
or `sin alpha=((AC)/(CB))sin 45^@`
`=(200sqrt2/400)1/sqrt2=1/2`
`:. alpha=30^@`
Therefore, the pilot should steer in a direction at an angle of `(45^@+alpha) or 75^@` from north towards east.
Further, `|v_a|/(sin(180^@-45^@-30^@))=400/sin 45^@`
or `|v_a|=(sin 105^@/sin 45^@)xx(400) km//h`
` = (cos 15^@/sin45^@)(400) km//h`
`=(0.9659/0.707)(400) km//h`
`:.` The time of journey from A to B is
`t=(AB)/|v_a|=1000/546.47 h`
`t=1.83 h`
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