(D) The time of flight $T$ is given by $T = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 \ s$.Let $v_b$ be the velocity of the ball and $v_u

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(D) The time of flight $T$ is given by $T = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 \ s$.Let $v_b$ be the velocity of the ball and $v_u$ be the velocity of the bullet after the collision.For the ball: $20 = v_b \times T \implies v_b = 20 \ m/s$.For the bullet: $100 = v_u \times T \implies v_u = 100 \ m/s$.Applying the law of conservation of linear momentum in the horizontal direction:$m_{bullet} V = m_{ball} v_b + m_{bullet} v_u$$0.01 \times V = 0.2 \times 20 + 0.01 \times 100$$0.01 V = 4 + 1$$0.01 V = 5$$V = 500 \ m/s$.

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Difficult

$A$ ball of mass $0.2 \ kg$ is at rest at a height of $5 \ m$. $A$ bullet of mass $0.01 \ kg$ moving horizontally with a velocity $V \ m/s$ strikes the center of the ball. After the collision,the ball and the bullet move independently. The ball hits the ground at a distance of $20 \ m$ and the bullet hits the ground at a distance of $100 \ m$ from the base of the pillar. What is the initial velocity $V$ of the bullet in $m/s$?

A
$250$
B
$250 \sqrt{2}$
C
$400$
D
$500$

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

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$A$ rubber ball is dropped from a height of $5 \ m$ on a planet,where the acceleration due to gravity is not known. On bouncing,it rises to $1.8 \ m$. The ball loses its velocity on bouncing by a factor of

EasyMHT CET 2007

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$A$ block $C$ of mass $m$ is moving with velocity $v_0$ and collides elastically with block $A$ of mass $m$ which is connected to another block $B$ of mass $2m$ through a spring of spring constant $k$. What is $k$ if $x_0$ is the compression of the spring when the velocity of $A$ and $B$ is the same?

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DifficultAIIMS 2010

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$A$ particle of mass $3 \ kg$ is moved slowly along the path $ABCDE$ from $A$ to $E$. The heights of $B$,$C$,and $D$ are $5 \ m$,$4 \ m$,and $6 \ m$ respectively. The total path length is $20 \ m$,the horizontal distance $AE = 10 \ m$,and the coefficient of friction $\mu = 0.6$. Calculate the work done in $J$ to slowly move the mass from $A$ to $E$. (Take $g = 10 \ m/s^2$)

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$A$ rubber ball is dropped from a height of $5 \ m$ on a planet,where the acceleration due to gravity is not known. On bouncing,it rises to $1.8 \ m$. The ball loses its velocity on bouncing by a factor of

$A$ ball loses $15.0\%$ of its kinetic energy when it bounces back from a concrete wall. With what speed must you throw it vertically down from a height of $12.4\, m$ to have it bounce back to the same height (ignore air resistance)? ............. $m / s$

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