Final answer:
The speed of the wind to a stationary observer, when considering the cyclist’s movement, is 10 km/h directed northwest. This is determined by performing vector addition and taking into account the components of the wind's and cyclist’s velocities.
Step-by-step explanation:
To determine the speed and direction of the wind to a stationary observer while considering a cyclist moving southeast at 15 km/h and a wind blowing from the southwest at 25 km/h, we need to perform vector addition.
First, we need to decompose the given velocities into their components. The cyclist’s velocity is southeast, which means it has both east and south components that are equal since southeast is directly between them. The wind's velocity from the southwest also has equal components to the north and east.
Since the wind is to the cyclist’s southwest, for the stationary observer, the south component of the cyclist’s velocity will partially negate the north component of the wind's velocity, while the east component of both the cyclist and the wind will add up. The resulting wind seen by the observer will then have a reduced speed in the north-south axis and an increased speed in the east-west axis.
Calculating the vector components and using the Pythagorean theorem, we find that the observer perceives the wind coming from the northwest with a speed of 10 km/h. Thus, the correct answer is (d) 10 km/h directed northwest.