A plane leaves toronto and flies with an airspeed of 360.0 km/h always pointing east. A wind is blowing at 65.0 km/h [S 35.0 degrees E]. What is the plane's velocity relative to the ground? What is the plane's displacement from Toronto after flying for 2.4 hours.

Most of us say where the wind is coming from but this seems to say that it is going S 35 E

u east = 360 + 65 sin 35
v south = 65 cos 35

|V| = sqrt (u^2 + v^2)
A = tan^-1 (u/v)
where A is angle east of south

x = distance E = u * 2.4
y = distance S = v *2.4
(D) = sqrt(x^2+y^2)
A is same old A

To find the plane's velocity relative to the ground, we need to consider the effect of the wind. We can use vector addition to calculate it.

1. Let's break down the wind velocity into its components. We know that the wind is blowing at 65.0 km/h [S 35.0° E].
- The south component of the wind can be calculated as s = 65.0 km/h * sin(35.0°).
- The east component of the wind can be calculated as e = 65.0 km/h * cos(35.0°).

2. Now, let's calculate the plane's relative velocity to the ground.
- Since the plane is flying east with an airspeed of 360.0 km/h, its velocity has an east component of 360.0 km/h and no south component.

3. To find the plane's relative velocity to the ground, we can add the components of the plane's velocity and the wind's velocity.
- The east component of the plane's velocity relative to the ground is 360.0 km/h + e.
- The south component of the plane's velocity relative to the ground is s.

4. Using the Pythagorean theorem, we can find the magnitude (speed) of the plane's velocity relative to the ground.
- The magnitude of the plane's velocity relative to the ground is given by the square root of the sum of the squares of its east and south components.
- It can be calculated as sqrt((360.0 km/h + e)^2 + s^2).

Now let's calculate the values:

1. Wind components:
- south component (s) = 65.0 km/h * sin(35.0°).
- east component (e) = 65.0 km/h * cos(35.0°).

2. Plane's velocity relative to the ground:
- east component of the plane's velocity relative to the ground = 360.0 km/h + e.
- south component of the plane's velocity relative to the ground = s.

3. Magnitude (speed) of the plane's velocity relative to the ground:
- magnitude = sqrt((360.0 km/h + e)^2 + s^2).

Now that we have the plane's velocity relative to the ground, we can calculate its displacement from Toronto after flying for 2.4 hours.

4. Displacement:
- Displacement = magnitude * time.

Let's calculate the values.