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Grade: 12
A plane takes t × 10*2 seconds to fly around a square with side a = 3.5 km, when the wind is blowing with a speed u = 30m/s parallel to the diagonal of the square. The velocity of plane in still air is v = 50 m/s. Find t.
3 years ago

Answers : (1)

Shaswata Biswas
132 Points
The velocity of the air is u = 30 m/s paralle to the diagonal. So its components along the sides of the squares are u= uy = 30÷\sqrt{}2. Now veoloccity of plane in stil air v = 50 m/s. 
When the plane is flying in the direction of the wind, total velocity, V+ = v+ux
And when it is flying opposite to the wind, its velocity is V- = v-ux
Now side of the square L = 3500 m
The plane wiil fly with the wind two sides, and oppsite to the wind two sides.
The tottal time taken, T = 2L÷V+ 2L÷V-
= 2×3500{1÷(50+30/\sqrt{}2) + 1÷(50-30/\sqrt{}2)} 
= 3.41×102
So the required value of t is 3.41.
3 years ago
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