1.

Aman is moving downward on an inclined plane (θ=37)with constant velocity v0 and rain drop appear to him moving in horizontal direction with velocity 2v0 towards him.If man increases his velocity to 2v0,the velocity of rain drops as observed by man is √n/5v0, then find n.

Answer»

The value of n is 41.

Explanation:

Let the relative velocity of man with respect to ground is  Vmg = Vm .
 Also, the relative velocity of rain w.r.t ground be Vrg = Vr .
And the relative velocity of rain with respect to man is Vrm .
We can say the relation between  Vm,  Vr,  Vrm as Vrm = Vr - Vm

Given,

V= v₀cos37°(-i) + v₀sin37°(-j) 

Vm = -4v₀/5 i - 3v₀/5 j 

and Vrm = 2v₀ i 

Hence, Vrm = Vr - Vm

Vr =2v₀i +(-4v₀/5 i - 3v₀/5 j) 

= 6v₀/5 i - 3v₀/5 j       ----(i)

Now, velocity of man with respect to ground, = -2v₀cos37° i - 2v₀sin37°j 

= -8v₀/5 i - 6v₀/5 j 

Vrm = 6v₀/5 i - 3v₀/5 j -(- 8v₀/5 i - 6v₀/5 j)

= 14v₀/5 i + 3v₀/5 j

Now, |Vrm | = √{(196 + 9)/25}v₀ = √{205/25}v₀ =√(41/5)v₀ 

Hence, from the above equation it is clear that  n =41



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