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A man is cycling at 4m/s. To him, rain appears to fall at 30 ° to vertical. If he doubles his velocity rain appears to fall at 60 ° to vertical. Find speed of rain.

A man is cycling at 4m/s. To him, rain appears to fall at 30° to vertical. If he doubles his velocity rain appears to fall at 60° to vertical. Find speed of rain.

Grade:11

1 Answers

Arun
25750 Points
3 years ago
Dear student
 
 
Velocity of rain wrt man= 4m/sat an angle 30º with vertical (given)
 
velocity of man wrt ground = 4m/s
 
from fig.
 
velocity of rain wrt man + velocity of man wrt ground = velocity of rain wrt ground (triangle law of vector addition)
 
so, velocity of rain wrt ground = √(4)2 + (4)2 + 2(4)(4)cos 120
 
                                          = √ 16+16+32(-0.5)
 
                                          =√32-16
 
                                          =√16 = 4m/s
 
hence proved

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