Question

Rain drops are falling downward with speed 30 km/h. A bus is moving in the horizontal direction with 40 km/hr. At what angle a
speed rain drops strike the vertical wind glass of bus?
(A) 50kmph, 0 = tan-1 (1)
(B) 50kmph, 0 = tan' ( )
(C) 70kmph, 0 = 45°
(D) 10kmph,
tan-1
G)​

Answer 1

Answer:

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Explanation:

With respect to car:

40 km/h=40×  

18

5

​  

m/s=  

9

100

​  

m/s

so tanθ=  

20

100/9

​  

=  

9

5

​  

 

⇒θ=tan  

−1

 

9

5

​  

 So (A) is correct

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Answer 2

Given:

Rain drops are falling downward with speed 30 km/h. A bus is moving in the horizontal direction with 40 km/hr.

To find:

Angle and speed at which raindrops strike the wind-screen of the bus.

Calculation:

Let Velocity of bus be v_(b) and Velocity of rain w.r.t Ground be v_(rg). So, the velocity of rain w.r.t bus will be v_(rb)

$\therefore \: v_{rb} = \sqrt{ {(v_{b})}^{2} + {(v_{rg})}^{2} }$

$= > \: v_{rb} = \sqrt{ {(40)}^{2} + {(30)}^{2} }$

$= > \: v_{rb} = \sqrt{ 1600+ 900 }$

$= > \: v_{rb} = \sqrt{2500 }$

$\boxed{ = > \: v_{rb} = 50 \: kmph}$

Let the angle in which rain is falling with the vertical be $\theta$:

$\therefore \: \tan( \theta) = \dfrac{v_{b}}{v_{rg}}$

$= > \: \tan( \theta) = \dfrac{40}{30}$

$= > \: \tan( \theta) = \dfrac{4}{3}$

$\boxed{ = > \: \theta= { \tan}^{ - 1} ( \dfrac{4}{3} )}$