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

Answer:

the magnitude of Vpg = 493.711 km/h

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 = $\sqrt{(42.025^2+(-491.92)^2)} km/h$

the magnitude of Vpg = 493.711 km/h