Answer:
[tex]v_{s}=65.2km/h[/tex]
Explanation:
Given data
Flight distance S=4890 km
Time difference Δt=t₂-t₁=40 min
Air speed of plane=980 km/h
To find
Speed of jet stream
Solution
When moving in the same direction as the jet stream time taken as t₁=d/(v+vs),v is velocity of plane and vs is velocity of plane
While moving in opposite direction t₂=d/(v+vs)
So
[tex]t_{2}-t_{1}=\frac{d}{(v-v_{s}) } - \frac{d}{(v+v_{s}) }\\t_{2}-t_{1}=\frac{d(v+v_{s})-d(v-v_{s})}{(v-v_{s})(v+v_{s})} \\t_{2}-t_{1}=\frac{2dv_{s}}{(v)^{2} -(v_{s})^{2} }\\0.666667h=\frac{2(4890km)v_{s}}{(980km/h)^{2} -(v_{s})^{2} }\\0.666667((980km/h)^{2} -(v_{s})^{2})=9780v_{s}\\640267-0.666667(v_{s})^{2}-9780v_{s}=0\\0.666667(v_{s})^{2}+9780v_{s}-640267=0[/tex]
Apply quadratic formula to solve for vs
So
[tex]v_{s}=65.2km/h[/tex]
