Question

To a motorist travelling due North at 50km/hr, the wind appears to come from North West at 60mk/hr. Find the true velocity of the wind.​

Answer 1

Answer:

The true velocity of wind will be 43.1 km/h.

Explanation:

Given that,

Velocity of motor $\vec{v_{m}}= 50\hat{j}\ km/h$

The resultant velocity of wind

$\ver{v_{r}}=60\hat{i}\times\dfrac{1}{\sqrt{2}}+60\hat{j}}\times\dfrac{1}{\sqrt{2}}$

Suppose, the true velocity of wind is $\vec{v_{w}}$.

We need to calculate the true velocity of wind

Using formula of resultant velocity

$\vec{v_{m}}+\vec{v_{w}}=\vec{v_{r}}$

$\vec{v_{w}}=\vec{v_{r}}-\vec{v_{m}}$

Where, $\vec{v_{m}}$ = velocity of motor

$\vec{v_{w}}$ = velocity of wind

$\vec{v_{r}}$ = resultant velocity

Put the value into the formula

$\vec{v_{w}}=\dfrac{60}{\sqrt{2}}\hat{i}+(\dfrac{60}{\sqrt{2}}-50)\hat{j}$

$\vec{v_{w}}=42.43\hat{i}-7.57\hat{j}$

The magnitude of true velocity is,

$v_{m}=\sqrt{(42.43)^2+(-7.57)^2}$

$v_{m}=43.0.9\approx 43.1\ km/h$

Hence,  The true velocity of wind will be 43.1 km/h.