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To a man walking at the rate of 4 km/h t...

To a man walking at the rate of 4 km/h the rain appears to fall vertically. When he increases his speed 8 km/h it appears to meet him at an angle of 45 with vertical. Find the angle made by the velocity of rain with the vertical and its value.

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To solve the problem, we need to analyze the situation using vector components and trigonometric relationships. Here's the step-by-step solution: ### Step 1: Understand the Problem A man is walking at two different speeds (4 km/h and 8 km/h) and observes the rain falling at different angles. When walking at 4 km/h, the rain appears to fall vertically, and when walking at 8 km/h, it appears to meet him at a 45-degree angle with the vertical. We need to find the angle made by the velocity of the rain with the vertical and its value. ### Step 2: Define Variables Let: - \( v_m1 = 4 \) km/h (velocity of the man when he walks at 4 km/h) ...
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