A ball of mass $$0.2$$ kg rests on a vertical post of height $$5$$ m. A bullet of mass $$0.01$$ kg, travelling with a velocity ν $$m/s$$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $$20$$ m and the bullet at a distance of $$100$$ m from the foot of the post. The initial velocity ν of the bullet is

Question

A ball of mass $$0.2$$ kg rests on a vertical post of height $$5$$ m. A bullet of mass $$0.01$$ kg, travelling with a velocity ν $$m/s$$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $$20$$ m and the bullet at a distance of $$100$$ m from the foot of the post. The initial velocity ν of the bullet is

Infinity Learn · Accepted Answer

Time taken by the bullet and ball to strike the ground $$ist=2hg=2.510=1sLet$$ ν$$1$$ and ν$$2$$ be the velocities of ball and bullet aftercollision. Then applying,x $$=$$ νtWe have, $$20=v1$$⋅$$1$$ or $$v1=20m/s100=v2.1$$ or $$v2=100m/sNow$$, from conservation of linear momentum before and after collision we have,$$0.01v=(0.2.20)+(0.01.100)On$$ solving, we getv $$=$$ $$500$$ m $$/$$ s.

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