To calculate the resultant velocity of the plane, we need to consider the two velocity components: the plane's velocity heading due north and the velocity of the wind blowing due west. These two components are perpendicular to each other.
Given that:
- The plane's northward velocity = 85 km/h (vertical component)
- The wind's westward velocity = 45 km/h (horizontal component)
Since these components are perpendicular, we can use the Pythagorean theorem to find the resultant velocity.
The correct choice is:
b. Since the two velocity components are perpendicular we can calculate the resultant velocity using the Pythagorean theorem.
The resultant velocity \( R \) can be calculated using the formula:
\[ R = \sqrt{(V_n)^2 + (V_w)^2} \]
Where \( V_n = 85 \) km/h (northward component) and \( V_w = 45 \) km/h (westward component).
So,
\[ R = \sqrt{(85)^2 + (45)^2} = \sqrt{7225 + 2025} = \sqrt{9250} \approx 96.2 , \text{km/h} \]
Thus, the resultant velocity of the plane is approximately 96.2 km/h.
0 answers