A plane is heading west at 200 mph. The wind is blowing S30°W at 25 mph.

1. what is the ground speed of the plane?

I could not figure this one out. Please help?

I could not figure this one out. Please help me.

To find the ground speed of the plane, we need to add the velocity of the plane and the velocity of the wind together. Let's break down the velocities into their horizontal and vertical components.

First, let's calculate the components of the wind velocity:

The wind is blowing in the direction S30°W (south 30 degrees west). This means that it is blowing 30 degrees to the left of south.

The horizontal component of the wind's velocity can be found using trigonometry: cos(30°) = adjacent/hypotenuse.
Adjacent = cos(30°) * 25 mph = 21.65 mph (approximately).

The vertical component of the wind's velocity can be found using trigonometry: sin(30°) = opposite/hypotenuse.
Opposite = sin(30°) * 25 mph = 12.5 mph.

Now, let's calculate the ground speed of the plane:

Since the plane is heading west at 200 mph, its horizontal speed is 200 mph, and its vertical speed is 0 mph.

To find the ground speed, we add the horizontal components of the plane and the wind together. So, the ground speed will be 200 mph (plane's horizontal speed) + 21.65 mph (wind's horizontal component) = 221.65 mph.

Therefore, the ground speed of the plane is approximately 221.65 mph.