An aeroplane flies along a straight line from `A` to `B` with a speed `v_(0)`. A steady wind `v` is blowing if `AB=l` then
a)total time for the trip is `(2v_(0)l)/(v_(0)^(2)-v^(2))` if wind blows along the line `AB`
b)total time for the trip is `2l/sqrt(v_(0)^(2)-v^(2))`,if wind blows perpendicular to the line `AB`
c)total time for the trip decrease because of the pressure of wind
d)total time for the trip increase because of the presence of wind

Options

A. `a,b,d` are correct
B. `a,b,c` are correct
C. only `a,d` are correct
D. only `b,d` are correct

Answer

A

Explanation

a,b,d are correct When wind blows along the line `AB`,
`t=t_(ArarrB)+t_(BrarrA)`
`rArrt=l/(v+v_(0))+l/(v_(0)-v)rArr t=(2lv_(0))/(v_(0)^(2)-v^(2))`
`t=t_(ArarrB)+t_(BrarrA)`
`v^(t)=sqrt(v_(0)^(2)-v^(2)) v^(t)=sqrt(v_(0)^(2)-v^(2))`
`t_(ArarrB)=l/sqrt(v_(0)^(2)-v^(2)) t_(BrarrA)=l/sqrt(v_(0)^(2)-v^(2))`
Hence `t=(2l)/sqrt(v_(0)^(2)-v^(2))`
If the wind were not present then total time taken for the trip would have been `t=(2l)v^(0)` i.e. the total time for the trip increases because of the presence of wind