A plane is flying west at 214 km/h. The wind is blowing south at 108km/h. a what is the ground speed of the plane
b In what direction does the plane travel
hgiy
To find the ground speed of the plane, we can use vector addition. The ground speed will be the magnitude of the resultant vector obtained by adding the velocity of the plane to the velocity of the wind.
Let's represent the westward direction as the negative x-axis, and the southward direction as the negative y-axis.
a) To find the ground speed of the plane:
The velocity of the plane flying west at 214 km/h can be represented as (214 km/h, 0 km/h) since there is no north or south component to its velocity.
The velocity of the wind blowing south at 108 km/h can be represented as (0 km/h, -108 km/h) since there is no east or west component to the wind's velocity.
To find the resultant vector, we add the corresponding components:
Resultant vector = (214 km/h + 0 km/h, 0 km/h - 108 km/h)
= (214 km/h, -108 km/h)
The magnitude of the resultant vector gives us the ground speed of the plane:
Ground speed = √((214 km/h)² + (-108 km/h)²)
= √(45796 km²/h² + 11664 km²/h²)
≈ √57460 km²/h²
≈ 239.9 km/h
Therefore, the ground speed of the plane is approximately 239.9 km/h.
b) To find the direction in which the plane travels:
We can use trigonometry to find the angle between the resultant vector and the negative x-axis.
Direction angle = arctan((-108 km/h) / (214 km/h))
= arctan(-0.5047)
≈ -26.56°
Since we are using the negative x-axis as the westward direction, the direction of the plane's travel is 26.56° west of south.
Therefore, the plane travels in a direction approximately 26.56° west of south.