A ball of mass $0.2 \ kg$ rests on a vertical post of height $5 m$. A bullet of mass $0.01 \ kg$, traveling with a velocity $V / s$ 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 $V$ of the bullet is
A ball of mass $0.2 \ kg$ rests on a vertical post of height $5 m$. A bullet of mass $0.01 \ kg$, traveling with a velocity $V / s$ 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 $V$ of the bullet is
- [IIT 2011]
- A
$250 \ m / s$
- B
$250 \sqrt{2} \ m / s$
- C
$400 \ m / s$
- D
$500 \ m / s$
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- [JEE MAIN 2024]
A shell is fired at a speed of $200\ m/s$ at an angle of $37^o$ above horizontal from top of a tower $80\ m$ high. At the same instant another shell was fired from a jeep travelling away from the tower at a speed of $10\ m/s$ as shown. The velocity of this shell relative to jeep is $250\ m/s$ at an angle of $53^o$ with horizontal. Find the time (in $sec$) taken by the two shells to come closest.
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Two particles are projected from a tower in opposite directions horizontally with speed $10\,m / s$ each. At $t=1\,s$ match the following two columns.
Column $I$
Column $II$
$(A)$ Relative acceleration between two
$(p)$ $0$ SI unit
$(B)$ Relative velocity between two
$(q)$ $5$ SI unit
$(C)$ Horizontal distance between two
$(r)$ $10$ SI unit
$(D)$ Vertical distance between two
$(s)$ $20$ SI unit
Two particles are projected from a tower in opposite directions horizontally with speed $10\,m / s$ each. At $t=1\,s$ match the following two columns.
| Column $I$ | Column $II$ |
| $(A)$ Relative acceleration between two | $(p)$ $0$ SI unit |
| $(B)$ Relative velocity between two | $(q)$ $5$ SI unit |
| $(C)$ Horizontal distance between two | $(r)$ $10$ SI unit |
| $(D)$ Vertical distance between two | $(s)$ $20$ SI unit |
An aeroplane is flying horizontally with a velocity of $600\, km/h$ at a height of $1960\, m$. When it is vertically at a point $A$ on the ground, a bomb is released from it. The bomb strikes the ground at point $B$. The distance $AB$ is
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