An airplane traveling east at a speed of 270 km/h encounters a wind of 75 km/h what is the resulting speed of the plane if:

- The wind is blowing east.
- The wind is blowing west.
- The wind is blowing north.

************* CLICK ON MY NAME TO SEE IF YOU CAN HELP ME WITH ANY OTHER QUESTIONS PLEASEEEEEE ***************************

Airplane speed = <270,0>

(components in the x,y directions)

Wind speed 75 km/hr eastwards
=<75,0>

Resultant speed
= <270,0>+<75,0> = <345,0>
= 345 km/hr eastwards.

Wind speed blowing 75 km/h west
Resultant
=<270,0>+<-75,0>
=<195,0>
=195 km/hr eastwards

Wind blowing north
Resultant speed
=<270,0>+<0,75>
=<270,75>
=√(270²+75²)
=280.2 km/h approximately

Thank you so much for your help, I was stuck on this question forever!

You're welcome!

To find the resulting speed of the plane in each scenario, we can use vector addition. The magnitude of the resulting velocity can be found using the Pythagorean theorem. Here's how:

1. Wind is blowing east:
In this case, the wind and the plane are moving in the same direction. To find the resulting speed, we need to add the magnitudes of the plane's speed and the wind's speed together. So, 270 km/h (plane's speed) + 75 km/h (wind's speed) = 345 km/h.

2. Wind is blowing west:
When the wind is blowing in the opposite direction of the plane, we need to subtract the magnitude of the wind's speed from the plane's speed to find the resulting speed. So, 270 km/h (plane's speed) - 75 km/h (wind's speed) = 195 km/h.

3. Wind is blowing north:
In this scenario, the wind's direction is perpendicular to the plane's direction. Therefore, the wind's speed does not affect the speed of the plane. The resulting speed would still be 270 km/h, as the wind is blowing perpendicular to the plane's path.

So, the resulting speed of the plane is:
- 345 km/h when the wind is blowing east.
- 195 km/h when the wind is blowing west.
- 270 km/h when the wind is blowing north (or any other direction perpendicular to the plane's path).