Question

If a plane has an airspeed of 40 m/s and is experiencing a crosswind of 30 m/s, what is its ground speed in m/s?

Answer 1

Answer:50
`ms^(-1)`

Step-by-step explanation:

Let
`v_(a)` be the airspeed.

Let
`v_(w)` be the cross wind speed.

We know that,ground speed is the vector sum of airspeed and cross wind speed and airspeed is perpendicular to cross wind speed.

If
`v_(1)` and
`v_(2)` are two perpendicular vectors,the resultant vector has the magnitude
`\sqrtv`

Given,

`v_(a)=40ms^(-1)\\v_(c)=30ms^(-1)`

So,the ground speed is
`\sqrt{40^(2)+30^(2)}=√(2500)=50ms^(-1)`