Answer:
[tex]V_{A/E}=55.23km/h\\or\\V_{A/E}=15.342m/s[/tex]
Explanation:
The velocity of plane relative to earth is given by:
[tex]V_{P/E}=\frac{d}{t}\\V_{P/E}=\frac{[-121i-20j]km}{0.490h} \\V_{P/E}=[-247i-41j]km/h[/tex]
As the from given data.The velocity of plane relative to air is:
[tex]V_{P/A}=[-210i]km/h[/tex]
According to relative motion of velocity of the air relative to earth given by:
[tex]V_{A/E}=V_{P/E}-V_{P/A} \\V_{A/E}=[(-247i-41j)km/h]-(-210i)km/h\\V_{A/E}=[-37i-41j]km/h\\[/tex]
The magnitude is given as:
[tex]V_{A/E}=\sqrt{(37)^{2}+(41)^{2} }\\ V_{A/E}=55.23km/h\\or\\V_{A/E}=15.342m/s[/tex]
Answer:
55km/h , 47.87° south west or 227.87°
Explanation:
If there is no wind then the plane would be at a distance
d=(210 km/h)(0.49h) = 102.9 km west of the starting point.
if the wind is blown then then the plane is 121 km - 102.9 km = 18.1 km west and 20 km south in the time 0.49 h.
Velocity of the plane in west direction=(18.1 km) / 0.49 h = 36.9 km/h
velocity of the plane in south direction=(20 km) / 0.49 h = 40.8 km/h
Now the wind velocity is
[tex]\sqrt{(36.9^2 + 40.8^2}[/tex]
= 55.01 km/h
The direction is
θ =tan⁻¹ (40.8 / 36.9)
θ = 47.87° south west or 227.87°
