Question

An airplane is heading due south at a speed of 560 km/h . If a wind begins blowing from the southwest at a speed of 80.0 km/h (average). Calculate magnitude of the plane's velocity, relative to the ground.

Answer 1

the magnitude of Vpg = 493.711 km/h

Step-by-step explanation:

given data

speed Vpg = 560 km/h

speed Vwg = 80 km/h

solution

we get here magnitude of the plane velocity w.r.t. ground is

we know that the Vpg = Vpw + Vwg .....................1

writing the component of the velocity that is

Vpw = (0 km/h î - 560 km/h j )

Vwg = (80 cos 45 km/h î + 80 sin 45 km/h j)

adding these

Vpg = (0+80 cos 45 km/h ) î + ( -560 + 80 sin 45 km/h j)i

Vpg = (42.025 ) î (-491.92 km/h)j

now we take magnitude

the magnitude of Vpg =
`√((42.025^2+(-491.92)^2)) km/h`

the magnitude of Vpg = 493.711 km/h