Answer:
The true velocity of wind will be 43.1 km/h.
Explanation:
Given that,
Velocity of motor [tex]\vec{v_{m}}= 50\hat{j}\ km/h[/tex]
The resultant velocity of wind
[tex]\ver{v_{r}}=60\hat{i}\times\dfrac{1}{\sqrt{2}}+60\hat{j}}\times\dfrac{1}{\sqrt{2}}[/tex]
Suppose, the true velocity of wind is [tex]\vec{v_{w}}[/tex].
We need to calculate the true velocity of wind
Using formula of resultant velocity
[tex]\vec{v_{m}}+\vec{v_{w}}=\vec{v_{r}}[/tex]
[tex]\vec{v_{w}}=\vec{v_{r}}-\vec{v_{m}}[/tex]
Where, [tex]\vec{v_{m}}[/tex] = velocity of motor
[tex]\vec{v_{w}}[/tex] = velocity of wind
[tex]\vec{v_{r}}[/tex] = resultant velocity
Put the value into the formula
[tex]\vec{v_{w}}=\dfrac{60}{\sqrt{2}}\hat{i}+(\dfrac{60}{\sqrt{2}}-50)\hat{j}[/tex]
[tex]\vec{v_{w}}=42.43\hat{i}-7.57\hat{j}[/tex]
The magnitude of true velocity is,
[tex]v_{m}=\sqrt{(42.43)^2+(-7.57)^2}[/tex]
[tex]v_{m}=43.0.9\approx 43.1\ km/h[/tex]
Hence, The true velocity of wind will be 43.1 km/h.
