Question

find the velocity at which a rifle bullet must be fired vertically so as to reach a height of 1km. what time will elapse before the bullet passes through the firing point om its return journey?(g=9.8m/s)​

Answer 1

Given that,

Height = 1 km

We need to calculate the velocity

Using conservation of energy

$K.E=P.E$

$\dfrac{1}{2}mv^2=mgh$

$v^2=2gh$

$v=\sqrt{2gh}$

Where, v = velocity

h = height

g = acceleration due to gravity

Put the value into the formula

$v=\sqrt{2\times9.8\times1000}$

$v=140\ m/s$

For upward,

We need to calculate the time

Using equation of motion

$s=ut+\dfrac{1}{2}gt^2$

Put the value into the formula

$1000=140t+\dfrac{1}{2}\times9.8t^2$

$4.9t^2+140t-1000=0$

$t=5.9\ sec$....(I)

For downward,

We need to calculate the time

Using equation of motion

$s=ut+\dfrac{1}{2}gt'^2$

Put the value into the formula

$1000=0+\dfrac{1}{2}\times9.8t'^2$

$4.9t'^2=1000$

$t'^2=\dfrac{1000}{4.9}$

$t'=\sqrt{\dfrac{1000}{4.9}}$

$t'=14.28\ sec$....(II)

We need to calculate the total time elapsed

Using equation (I) and equation (II)

$t''=t+t'$

Put the value into the formula

$t''=5.9+14.28$

$t''=20.18\ sec$

Hence, The velocity is 140 m/s.

The total time elapsed is 20.18 sec.