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Studentka2010 [4]
3 years ago
5

To a man running east at the rate of 3m/s vain appears to fall vertically with a speed of 4m/s. Find the actual speed and direct

ion of rain...​
Physics
1 answer:
maria [59]3 years ago
5 0

Answer:

The actual speed of the rain is 5 m/s and its direction is -53.13°

Explanation:

The actual speed of the rain V = speed of man, v + speed of rain relative to man, v'.

V = v + v'

We add these vectorially.

Since the man's speed is 3 m/s east, in the positive x - direction, we have v = 3i  and the rain's speed is falling vertically at 4 m/s, in the negative y- direction, we have v' = -4j

So, V = v + v'

V = 3i + (-4j)

V = 3i - 4j

So, the magnitude of V which is its speed is V = √(3² + (-4)²) = √(9 + 16) = √25 = 5 m/s

The direction of V, Ф = tan⁻¹(vertical component/horizontal component) = tan⁻¹(-4/3) = tan⁻¹(-4/3) = tan⁻¹(-1.333) = -53.13°

So, the actual speed of the rain is 5 m/s and its direction is -53.13°

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