Question

a cart is moving towards a fixed target with speed of v m/s a gun mounted on cart fires bullets at the rate of 5 per second. if the no of bullets received at target per second is 6 then find the value of n if the bullets are moving with nv​

Answer 1

Given : a cart is moving towards a fixed target with speed of v m/s a gun mounted on cart fires bullets at the rate of 5 per second. the no of bullets received at target per second is 6 . bullets are moving with nv​

To find : value of n  

Solution:

Bullets are travelling at nv m/s

Let say time taken to reach by 1st bullet = t sec

Then distance covered by bullet  = nv * t  m

Bullets are fired at rate of 5 bullets per sec

=> one bullet per 0.2 sec

Hence 6th bullet has been fired after 1.2 sec

But 6th bullet reached with in a interval of 1 sec of 1st bullet fired

Hence travel time of 6th bullet = t  - 1.2 + 1  

= t  - 0.2 sec

Distance covered by bullet in t - 0.2 sec  = nv (t - 0.2 )

=nvt  -  0.2nv  m

Hence Cart has covered  a distance of 0.2nv  m before firing bullet

Time taken = 1.2 Sec

Speed of Cart = v m/s

Distance covered = 1.2v  m

1.2v  = 0.2nv

=> n =  6  

value of n  = 6

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