Question

A plate of mass M is held in air by firing bullets each of mass m with same velocity in virtically upward direction. If n bullets are fired per minute and each bullet strikes the plate with speed v and rebounds with half of the speed with which it strikes the plate, then the speed with which bullets are striking the plate is ( full question in given figure ) solve by process

Answer 1

Answer:$v=\frac{20Mg}{nm}$

Explanation:

Given mass of bullet is m and that of Plate is M

now change in momentum of bullet will give the impulse imparted to Plate

initial Velocity of bullet is v in m/s

final velocity of bullet is $-\frac{v}{2}$

change in momentum of bullet is $=mv-(-m\frac{v}{2})$

$dP=\frac{3mv}{2}$

Now change in momentum is $Fdt$

$Fdt=dp$

$F=\frac{n}{60}\times \frac{3mv}{2}$

and F should balance the weight of Plate

$Mg=\frac{n}{60}\times \frac{3mv}{2}$

$v=\frac{20Mg}{nm}$

Answer 2

Answer:

20 mg /MN

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