A bullet is fired from a gun. The force on the bullet is given by F=600-2× 105t where F is in newton and t in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

Question

A bullet is fired from a gun. The force on the bullet is given by F=600-2× 105t where F is in newton and t in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet? (A)  text9 Ns (B)  text1 text.8 Ns (C)  text0 text.9 Ns (D)  text0 text.3 Ns

Tardigrade Admin · Accepted Answer

Given, F=600-2× 105 t=0 Longrightarrow t=3× 10- 3 s Impulese I= displaystyle ∫ 0t F ⋅ d t = displaystyle ∫ 03 × (10)- 3 (600 - 2 × (10)5 t) d t =[.600 t-105 t2].03 × 10- 3=0.9 Ns

Q. A bullet is fired from a gun. The force on the bullet is given by $F = 600 - 2 \times 1 0^{5} t$ where $F$ is in newton and $t$ in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

$9 Ns$

$1 .8 Ns$

$0 .9 Ns$

$0 .3 Ns$

Given, $F = 600 - 2 \times 1 0^{5} t = 0$
$⟹ t = 3 \times 1 0^{- 3} s$
Impulese $I = \int_{0}^{t} F \cdot d t$
$= \int_{0}^{3 \times (10)^{- 3}} (600 - 2 \times (10)^{5} t) d t$
$= [600 t - 1 0^{5} t^{2}]_{0}^{3 \times 1 0^{- 3}} = 0.9 N s$

Q. A bullet is fired from a gun. The force on the bullet is given by F=600−2×105t where F is in newton and t in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

9 Ns

1.8 Ns

0.9 Ns

0.3 Ns