Final answer:
The velocity of the plane relative to someone standing on the ground is approximately 316.25 km/hr in a direction 5.35 degrees West of South.
Step-by-step explanation:
To determine the velocity of the plane relative to someone standing on the ground, we need to consider the vector addition of the plane's velocity and the crosswind's velocity. The magnitude of the resulting velocity vector can be found using the Pythagorean theorem, which states that the magnitude of the resulting velocity is equal to the square root of the sum of the squares of the two component velocities. The direction of the resulting velocity can be found using trigonometry by taking the inverse tangent of the ratio of the magnitudes of the component velocities.
In this case, the magnitude of the plane's velocity is 315 km/hr, and the magnitude of the crosswind's velocity is 30 km/hr. Using the Pythagorean theorem, we can find the magnitude of the resulting velocity:
Magnitude of resulting velocity = sqrt(315^2 + 30^2) = sqrt(99225 + 900) = sqrt(100125) = 316.25 km/hr
The direction of the resulting velocity can be found using trigonometry:
Direction of resulting velocity = arctan(30/315) ≈ 5.35 degrees West of South
Therefore, the velocity of the plane relative to someone standing on the ground is approximately 316.25 km/hr in a direction 5.35 degrees West of South.