Question

A train of length l moves with a constant speed v.a person at the back of the train fires a bullet at time t=0 towards a target which is at a distance of d from the front of the train ( on the same direction of the motion ) another person at yhe front of the train fires another bullet at time t=t towards the same target .both bullets reach the target at the same time .assuming the speed if the bullet is same.what is thwe length of the train?

Answer 1

we may assume that, when the person at the front of the train fires the bullet

the bullet fired by the person at the rear end has just reached this men

therefore;

using concept of relative velocity

T=(lengthof the train)/(Vb-Vt)

Answer 2

Given: Length of train = l

           Constant speed = v

            Bullet fired at time t = 0

            Distance between the person and the target = d

            Bullet fired by another person at time = t

            Both the bullets reach the target at the same time

To find: Length of the train

Solution:

Both people's bullets hit the target at the same moment, therefore we equate time to get,

$\frac{L-D}{V_{b} - V_{t} } = \frac{D}{V_{b} - V_{t}} + T\\\frac{L}{V_{b} - V_{t} } = \frac{D}{V_{b} + V_{t}} + \frac{D}{V_{b} - V_{t}} + T\\\frac{L}{V_{b} - V_{t} } = \frac{D(V_{b} - V_{t}+V_{b} + V_{t}) }{V_{b}^2 - V_{t}^2} +T\\\frac{L}{V_{b} - V_{t} } = \frac{2V_{b}D }{V_{b}^2 - V_{t}^2} = T\\L = \frac{2V_{b}D}{V_{b} + V_{t}} + T(V_{b} - V_{t})$

Hence, the length of the train is $L = \frac{2V_{b}D}{V_{b} + V_{t}} + T(V_{b} - V_{t})$

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