A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45° to the vertical. What is the speed of the rain? In what direction does rain fall as observed by a ground based observer?
A girl riding a bicycle with a speed of 5 m/s towards north direction, observes rain falling vertically down. If she increases her speed to 10 m/s, rain appears to meet her at 45° to the vertical. What is the speed of the rain? In what direction does rain fall as observed by a ground based observer?
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1 Answer
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This is a Long Answer Type Question as classified in NCERT Exemplar
Explanation – Vr= a? +b?
Velocity vg= 5m/s
Velocity of rain w.r.t girl = Vr-Vg= a? +b? -5?
= (a-5)? +b?
a-5=0, a=5
case II
vg = 10m/s?
Vrg= Vr - Vg
= a? +b? -10? = (a-10)? +b?
Rain appear to be fall at 45 degree so = b/a-10 =1
So b =-5
Velocity of rain = a? +b?
Vr = 5? -5?
Speed of rain Vr=
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Please find the solution below:
after 10 kicks,
v? = 3tî v? = 24cos 60°î + 24sin 60°? = 12î + 12√3?
v? = v? – v? = (12 – 3t)î + 12√3?
It is minimum when 12 - 3t = 0 ⇒ t = 4sec
ω = θ² + 2θ
α = (ωdω)/dθ = (θ² + 2θ) (2θ + 2)
At θ = 1rad.
ω = 3rad/s and α = 12rad/s²
a? = αR = 12 m/s² a? = ω²R = 9 m/s² A? = √ (a? ² + a? ²) = 15 m/s²
a? = v? ²/4r
a_A? = (v? ²/r²) × r = v? ²/r
a_A = 3v? ²/4r
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