Given:
The distance traveled by helicopter against the headwind, d₁=450 miles
The speed of the wind, w=35 mph
The distance traveled by helicopter the tailwind, d₂=702 miles
To find:
The speed of the helicopter.
Explanation:
Let us assume that the time it takes for the helicopter to travel the distances is t
The time duration for an object to cover a distance is given by,
[tex]T=\frac{d}{u}[/tex]
Where t is the time, d is the distance, and u is the velocity.
As the time it takes for the helicopter to cover the distances d₁ and d₂ are the same,
[tex]\frac{d_1}{v-w}=\frac{d_2}{v+w}[/tex]
Where v-w is the total speed of the helicopter when it is flying against the headwind and v+w is the speed of the helicopter when it is flying with a tailwind.
On substituting the known values,
[tex]\begin{gathered} \frac{450}{v-35}=\frac{702}{v+35} \\ \implies450v+15750=702v-24570 \\ 15750+24570=(702-450)v \\ \implies v=\frac{40320}{252} \\ =160\text{ m/s} \end{gathered}[/tex]
Final answer:
Thus the speed of the helicopter is 160 m/s
