Question

A bird flies with a speed u over a train which moves with a speed V the average speed of the boat with respect to train is travelling to and fro along the train the end to end is

Answer 1

Answer:

$( {u }^{2} - {v}^{2} ) \frac{1}{u}$

HOPE THIS HELPS YOU

Answer 2

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.