Question

A bird flies with a velocity u over a train which moves with a velocity v. The average speed of the bird in traveling to and fro along the train (end to end) is:
(b) 2uv/u+v
(b) in root v^2+u^2 (c) in root uv u^2-v^2/U​

Answer 1

Answer:

$\frac{u^2-v^2}{u}$

Step-by-step explanation:

Velocity of the train = v

Velocity of the bird = u

Let the length of the train is d

When the bird flies over the train in the direction of moving the train then w.r.t the train, the velocity of the bird will be = u - v

Time taken in travelling the distance d = d/(u-v)

Similarly, when the bird files over the train opposite to the direction of motion of the train then the velocity of the bird will be  = u + v

Time taken in travelling the distance d = d/(u+v)

Total time taken

$=\frac{d}{u-v}+\frac{d}{u+v}$

$=d[\frac{1}{u-v}+\frac{1}{u+v}]$

$=d[\frac{2u}{u^2-v^2}]$

In to and fro motion, total distance travelled by the bird = d + d = 2d

Average speed of the bird

= Total Distance/Total Time

= $\frac{2d}{2ud/(u^2-v^2)}$

= $\frac{u^2-v^2}{u}$

Hope this is helpful.