Question

In the fuse wire of a diwali bomb, the flame
propagates with constant velocity vf=0.8 cm/s.
What is the minimum length of the fuse a man
should have so that he can run off to a safe distance
of 120 m after igniting the flame, while the flame
will not reach the bomb? The speed of person is
vP=4 m/s.

Answer 1

Given that,

Safe distance = 120 m

Velocity of person = 4 m/s

Velocity of flame = 0.8 cm/s

We need to calculate the time taken by person

Using formula of time

$t=\dfrac{d}{v}$

Where, d = distance

v = velocity

t = time

Put the value into the formula

$t=\dfrac{120}{4}$

$t=30\ sec$

We need to calculate the minimum length of the fuse a man

Using formula of distance

$v_{f}=\dfrac{l}{t}$

$l=v_{f}\times t$

$l=0.8\times30$

$l=24\ cm$

Hence, The minimum length of the fuse is 24 cm.

Answer 2

Given that,

Safe distance = 120 m

Velocity of person = 4 m/s

Velocity of flame = 0.8 cm/s

We need to calculate the time taken by person

Using formula of time

$t=\dfrac{d}{v}$

Where, d = distance

v = velocity

t = time

Put the value into the formula

$t=\dfrac{120}{4}$

$t=30\ sec$

We need to calculate the minimum length of the fuse a man

Using formula of distance

$v_{f}=\dfrac{l}{t}$

$l=v_{f}\times t$

$l=0.8\times30$

$l=24\ cm$

Hence, The minimum length of the fuse is 24 cm.