Final answer:
The airplane's actual speed is 207.70 km/h and the magnitude of the vertical component of its velocity is 53.42 km/h.
Step-by-step explanation:
The actual speed of the airplane can be found by using the horizontal component of its velocity. In this case, the horizontal component is 200 km/h. Since the horizontal component is adjacent to the angle of 15 degrees, we can use the cosine function to find the actual speed, which is the hypotenuse of the triangle.
So, using the cosine function: cos(15) = Adjacent/Hypotenuse. Plugging in the values, we get cos(15) = 200 km/h / Hypotenuse. Solving for Hypotenuse, we find: Hypotenuse = 200 km/h / cos(15) = 207.70 km/h.
The magnitude of the vertical component of the airplane's velocity can be found using the sine function. Again, since the vertical component is the opposite side of the angle of 15 degrees, we can use the sine function.
So, using the sine function: sin(15) = Opposite/Hypotenuse. Plugging in the values, we get sin(15) = Opposite / 207.70 km/h. Solving for Opposite, we find: Opposite = 207.70 km/h * sin(15) = 53.42 km/h.