A plane flies at 150m/s at 35 degrees east of north. It encounters a wind from the west blowing 26 m/s.
and what is the question?
To find the actual velocity of the plane, we need to consider the effect of the wind on its motion. We can break down the plane's velocity into two components: one in the north direction and one in the east direction.
Given that the plane is flying at 150 m/s at 35 degrees east of north, we can use trigonometry to find the north and east components of its velocity.
The north component of the plane's velocity can be calculated as:
Vn = V * cos(theta)
where Vn is the north component, V is the velocity of the plane (150 m/s), and theta is the angle east of north (35 degrees).
The east component of the plane's velocity can be calculated as:
Ve = V * sin(theta)
where Ve is the east component.
Using these formulas, we can calculate the north and east components of the original velocity:
Vn = 150 * cos(35)
Ve = 150 * sin(35)
Now, let's consider the wind blowing from the west at 26 m/s. The wind's velocity will be represented as negative since it opposes the plane's motion.
The west component of the wind's velocity is -26 m/s.
To find the actual velocity of the plane, we add the north and east components of its original velocity to the west component of the wind's velocity:
Actual Velocity = (Vn + West Component of Wind's Velocity) i + Ve j
Substituting the values:
Actual Velocity = (150 * cos(35) - 26) i + (150 * sin(35)) j
Now you can calculate the magnitude and direction of the actual velocity.