An airplane has to fly eastward to a destination 856 km away. If wind is blowing at 18.0 m/s northward and the air speed of the plane is 161 m/s, in what direction should the plane head to reach its destination?
To determine the direction in which the plane should head, we need to consider the effect of the wind on the plane's flight. We can break down the given information as follows:
1. Wind speed: The wind is blowing at a speed of 18.0 m/s northward.
2. Airspeed of the plane: The airspeed of the plane is given as 161 m/s.
To find the direction in which the plane should head, we will use vector addition. The resultant vector, which represents the plane's actual velocity when accounting for the wind, will point from the starting position to the destination.
Since the plane needs to fly eastward, we can represent its required direction as due east. Let's break down the wind velocity into components:
- Wind velocity in the north direction: 18.0 m/s
- Wind velocity in the east direction: 0 m/s (since the wind is blowing northward)
Next, we'll consider the airspeed components of the plane:
- Airspeed in the east direction: 161 m/s
- Airspeed in the north direction: 0 m/s (since the plane is not moving in this direction)
Now, we can add the respective components to find the resultant velocity:
- Resultant velocity in the east direction: 161 m/s + 0 m/s = 161 m/s
- Resultant velocity in the north direction: 0 m/s + 18.0 m/s = 18.0 m/s
Therefore, the plane should head in the direction east of north (or 0 degrees east of north) to reach its destination.
To determine the direction in which the airplane should head to reach its destination, we need to consider the effect of wind on the plane's motion.
Let's break down the given information:
- The destination is 856 km away (no information about its direction is provided).
- The wind is blowing at 18.0 m/s northward.
- The airspeed of the plane is 161 m/s.
To find the direction, we can use vector addition. The plane's velocity is the sum of its airspeed and the wind's velocity. Since the wind is blowing northward, we can consider its velocity as (0 m/s, 18.0 m/s). The velocity of the plane is (161 m/s, 0 m/s) since it is moving eastward.
Adding these vectors together gives us the resulting velocity vector, which represents the direction and speed at which the plane will move:
Resulting velocity = (161 m/s + 0 m/s, 0 m/s + 18.0 m/s)
= (161 m/s, 18.0 m/s)
So, the resulting velocity vector is (161 m/s, 18.0 m/s).
To find the direction, we can calculate the angle made by the resulting velocity vector with respect to the eastward direction (x-axis). This can be done using trigonometry.
Angle = arctan(18.0 m/s / 161 m/s)
≈ arctan(0.1118)
≈ 6.39 degrees
Therefore, the plane should head in a direction approximately 6.39 degrees north of east to reach its destination.