Question

Rain is falling vertically when car is at rest. When car moves with a speed v rain appears at 60° with horizontal when car moves with speed(β+1)v rain appears 45° with the horizontal. find the value of β?

Answer 1

It has given that rain is falling vertically when car is at rest.

To find : the value of β

solution : case1 : when car moves with v , rain appears at 60° with horizontal.

so, tan60° = v_rg/v [ see figure ]

⇒√3v = v_rg ........(1)

case2 : when car moves with (β + 1)v, rain appears at 45° with horizontal.

so, tan45° = v_rg/(β + 1)v [ see figure ]

⇒(β + 1)v = v_rg .........(2)

dividing equation (1) by equation (2) we get,

√3/(β + 1) = 1

⇒β + 1 = √3

⇒β = √3 - 1 = 1.732 - 1 = 0.732

Therefore the value of β will be 0.732

Answer 2

AnswEr:-

Given:-

Rain is falling vertically when car is at rest. When car moves with a speed v rain appears at 60° with horizontal when car moves with speed(β+1)v rain appears 45° with the horizontal.

To find :-  the value of β

Solution :-

case1 : when car moves with v , rain appears at 60° with horizontal.

tan60° = v_rg/v

⇒√3v = v_rg ........(1)

case2 : when car moves with (β + 1)v, rain appears at 45° with horizontal.

tan45° = v_rg/(β + 1)v

⇒(β + 1)v = v_rg .........(2)

=> (1) / (2) we get,

=> √3/(β + 1) = 1

⇒β + 1 = √3

⇒β = √3 - 1 = 1.732 - 1 = 0.732

Hence,  the value of β is 0.732.

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