Question

9. A man running on a horizontal road at 8 km/h finds the
rain falling vertically. He increases his speed to 12 km/h
and finds that the drops make angle 30° with the vertical.
Find the speed and direction of the rain with respect to
the road.​

Answer 1

Answer:

sqrt{112}

Explanation:

According to question,when man moves with velocity 8 km/hr in x direction the rain falls vertically,

That means rain have horizontal component of 8 km/hr,

Let v be vertical component then the rain vector will =8i+vj  

Now, if he increase his speed to 12 km/hr, rain will form 30 angle with vertical and relative velocity of man w.r.t rain in horizontal component will become 12 km/hr-8 km/hr=4 km/hr

Now tan 30=4/v

thus, v=4 cot 30=4sqrt{3}

So velocity of rain wrt road is 8i-4sqrt{3}.

Its magnitude is sqrt(112)

Answer 2

Answer:

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