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A bird....................wind
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Greetings,
The answer to your question is typed below ↓
_____________________________________________
For this problem we use relative velocity concept..
Firstly -
_______________________________________________
Given:
time (1) : 2 h 30 min ----> 9000 sec
time (2) : 4 h 30 min ----> 16200 sec
distance : 45 km ----> 45000 m
_______________________________________________
Velocity of bird with respect to wind (flying in the same direction) [Vbw]
= Velocity of bird [Vb] - Velocity of wind [Vw]
∴ Vb = Vbw + Vw ----- 1
Velocity of bird with respect to wind (flying in the opposite direction) [Vbw]
∴ Vb = Vbw - Vw ----- 2
= Velocity of bird [Vb] - Velocity of wind [Vw]
Time (t1) = distance (d) ÷ (Vbw + Vw)
Time (t2) = distance (d) ÷ (Vbw - Vw)
____________________________________________
Using the above formulae we get equations 1 & 2.
t1 = d / (Vbw + Vw)
9000 = 45000 / (Vbw + Vw)
∴Vbw + Vw = 5 ------------ (i)
and similarly
16200 = 45000/ (Vbw-Vw)
∴ Vbw - Vw = 25/9
We then take simultaneous equations with (i) and (ii) :
Vbw + Vw = 5
Vbw - Vw = 25/9
Solving, we get
Vbw = 3.88 m/s
&
Vw = 1.11 m/s
And finally
as Vb = Vbw + Vw
Velocity of Bird in still air = 5 m/s
And
Speed of wind = 1.11 m/s
_____________________________________
P.S: Enjoy ;)
The answer to your question is typed below ↓
_____________________________________________
For this problem we use relative velocity concept..
Firstly -
_______________________________________________
Given:
time (1) : 2 h 30 min ----> 9000 sec
time (2) : 4 h 30 min ----> 16200 sec
distance : 45 km ----> 45000 m
_______________________________________________
Velocity of bird with respect to wind (flying in the same direction) [Vbw]
= Velocity of bird [Vb] - Velocity of wind [Vw]
∴ Vb = Vbw + Vw ----- 1
Velocity of bird with respect to wind (flying in the opposite direction) [Vbw]
∴ Vb = Vbw - Vw ----- 2
= Velocity of bird [Vb] - Velocity of wind [Vw]
Time (t1) = distance (d) ÷ (Vbw + Vw)
Time (t2) = distance (d) ÷ (Vbw - Vw)
____________________________________________
Using the above formulae we get equations 1 & 2.
t1 = d / (Vbw + Vw)
9000 = 45000 / (Vbw + Vw)
∴Vbw + Vw = 5 ------------ (i)
and similarly
16200 = 45000/ (Vbw-Vw)
∴ Vbw - Vw = 25/9
We then take simultaneous equations with (i) and (ii) :
Vbw + Vw = 5
Vbw - Vw = 25/9
Solving, we get
Vbw = 3.88 m/s
&
Vw = 1.11 m/s
And finally
as Vb = Vbw + Vw
Velocity of Bird in still air = 5 m/s
And
Speed of wind = 1.11 m/s
_____________________________________
P.S: Enjoy ;)
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