Final answer:
To find the plane's speed relative to the ground, we separate the wind's velocity into components and add the relevant ones to the plane's northward velocity. The northward component of the wind's velocity adds to the plane's speed, leading to an approximate ground speed of 281 km/h. The closest provided option is 270 km/h. Option B is correct.
Step-by-step explanation:
The student's question pertains to finding the plane's speed relative to the ground considering its own speed and the effect of wind. The airplane flies north at 235 km/h, and there is a wind blowing to the northeast at 65 km/h. To solve this, we can use vector addition, which involves separating the wind's velocity into its northward and eastward components before combining them with the plane's velocity.
Since the wind is blowing northeast (45° N of E), it has equal components in the north and east directions. Thus, both components of the wind's velocity are:
65 km/h * cos(45°) northward and 65 km/h * sin(45°) eastward, which both equal 65 km/h / \(√2\) or approximately 46 km/h.
Adding the wind's northward component to the plane's velocity, we get:
235 km/h + 46 km/h = 281 km/h (approximately) northward velocity.
Since the eastward component of the wind does not affect the northward speed, the plane's speed relative to the ground is approximately 281 km/h. Therefore, the closest answer from the options provided is B: 270 km/h.