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

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

Step-by-step 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}*(1)/(√(2))+60\hat{j}}*(1)/(√(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)}=(60)/(√(2))\hat{i}+((60)/(√(2))-50)\hat{j}`

`\vec{v_(w)}=42.43\hat{i}-7.57\hat{j}`

The magnitude of true velocity is,

`v_(m)=√((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.