Two trains each having a speed of 30km h

Asked by admin @ 20/08/2021 in Physics viewed by 295 People

Two trains each having a speed of 30 km/h are headed at each other on the same straight track. A bird

that can fly at 60 km/h flies off from one train when they are 60 km apart and heads directly for theother train. On reaching the other train it flies directly back to the first, and so forth.(a) How many trips the bird can make from one train to the other before they crash ?(6) What is the total distance the bird travels ?

Answered by admin @ 20/08/2021

Answer:

No. of trips = ∞

Total distance = 60 km.

Explanation:

Given :

Two train of speed 30 km / hr .

Speed of bird is 60 km / hr .

Given , distance between them is 60 m .

First , finding relative velocity of train A w.r.t train B

$\displaystyle{V_{AB}=30-(-30) \ km/hr}\\\\\\\displaystyle{V_{AB}=60 \ km/hr}$

Now time taken = displacement / velocity

Time taken = 60 km / 60 km / hr

Time taken = 1 hr .

Now relative velocity w.r.t Bird and train B.

$\displaystyle{V_{BB^{'}}=30-(-60) \ km/hr}\\\\\\\displaystyle{V_{BB^{'}}=90 \ km/hr}$

First tips t₁ time taken

Time taken = 60 / 90 [ 60 km distance given in question ]

Time taken = 2 / 3 hr .

Distance covers in t₁ time :

Distance = 60 × 2 / 3 km

Distance = 40 km .

Remaining distance = 60 - 40 = 20 km.

Second trips : t₂

Distance = 20 / 90 m

Distance = 2 / 3² m

We can see it is in form of GP.

$\displasystyle{Total \ trip = t_1 + t_2 +t_3 \ ..... \ t_n}$

$\displaystyle{T=\dfrac{2}{3}+\dfrac{2}{3^2} +\dfrac{2}{3^3} \ .... \ \dfrac{2}{3^n}}\\\\\\\displaystyle{T=\dfrac{2}{3}\left[1+\dfrac{1}{3} +\dfrac{1}{3^2} \ .... \ \dfrac{1}{3^{n-1}}\right]}\\\\\\\displaystyle{T=\dfrac{2}{3}\left[\dfrac{(1-(1/3)^n}{1-1/3}\right]}\\\\\\\displaystyle{T=1-\left(\dfrac{1}{3}\right)^n}$

But we already find that total time is taken 1 hr .

So the second term should be zero .

$\displaystyle{\left(\dfrac{1}{3}\right)^n=0}\\\\\\\displaystyle{3^n= \infty}\\\\\displaystyle{n= \infty}$

Thus the number of trips is infinite .

Total distance of bird :

Distance = velocity × time

Total distance of bird = 60 × 1 = 60 km

Hence we get answer .

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