To determine the true velocity of the wind, we need to find the vector sum of the motorcyclist's velocity and the wind velocity.
Let's break down the given information into vectors:
Motorcyclist's velocity (North) = 50 km/h
Wind velocity (Northwest) = 60 km/h
Since the wind is blowing from the Northwest, we can resolve it into its North and West components using trigonometry.
Given that the wind's velocity has a magnitude of 60 km/h, its North component can be found using the following equation:
North component = wind velocity * cos(angle)
Since the wind is blowing in a Northwest direction, the angle it makes with the North direction is 45 degrees. Therefore:
North component = 60 km/h * cos(45°)
North component = 60 km/h * √(2)/2
North component = 60√(2)/2 km/h
North component = 30√(2) km/h
To find the total velocity of the wind, we need to add the North and West components of the wind. Since the West component is 0 (the wind is not blowing in the East direction), the total velocity of the wind is equal to the North component alone.
Thus, the true velocity of the wind is 30√(2) km/h in the North direction.
To a motor cyclist traveling due North at 50km/h the wind appears to come from Northwest at 60km/h. What is the true velocity of the wind
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