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A gun of mass 20kg fires a bullet of mas...

A gun of mass `20kg` fires a bullet of mass `0.010kg` in a horizontal direction. If the gun recoils at `0.05ms^(-1)`, then calculate the velocity of the bullet. If the gun has to be stopped within a period of `0.1s` then what force should be exerted on the gun?

Text Solution

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Given , `m_(g)=20kg`, `m_(b)=0.010kg`, `v_(g)=-0.05ms^(-1)`
`v_(b)=?`, `t=0.1s`, `v=0`, `a=?`, `v=?`
Applying the law of conservation of momentum,
`0=m_(g)v_(g)+m_(b)v_(b)`
`:.0=-20xx0.05+0.010vb`
`:.v_(b)=(20xx0.05)/(0.01)=100ms^(-1)`
Applying `v=u+at`, `0=+0.05+a(0.1)`
i.e. `a=-(0.05)/(0.1)` `a=-5xx10^(-1)ms^(-2)`
`:.` Resistive force exerted on the gun by a shooter `=ma=20xx5xx10^(-1)=10N`
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