$A$ body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$ in $m/s$?

Two trolleys of mass $m$ and $3m$ are connected by a spring. They are compressed and released; once released,they move off in opposite directions and come to rest after covering distances $S_1$ and $S_2$ respectively. Assuming the coefficient of friction to be uniform,the ratio of distances $S_1:S_2$ is:

The velocity of the bullet becomes one-third after it penetrates $4 \ cm$ in a wooden block. Assuming that the bullet faces a constant resistance during its motion in the block,the bullet stops completely after traveling a total distance of $(4+x) \ cm$ inside the block. The value of $x$ is $.....$ (in $cm$)

$A$ man of mass $60 \ kg$ gets $10^5 \ calories$ of energy from food. If his efficiency is $28\%$,up to what height in $m$ can he climb?

Starting from rest on her swing at initial height $h_0$ above the ground,Saina swings forward. At the lowest point of her motion,she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$. She then swings backward and when reaching the lowest point of motion again,she simply lets go of the bag,which falls freely. Saina's backward swing then reaches maximum height $h_2$. Neglecting air resistance,how are the three heights related?

$A$ block of mass $1.9\, kg$ is at rest at the edge of a table of height $1\, m$. $A$ bullet of mass $0.1\, kg$ collides with the block and sticks to it. If the velocity of the bullet is $20\, m/s$ in the horizontal direction just before the collision,then the kinetic energy just before the combined system strikes the floor is $....J$. (Take $g = 10\, m/s^2$. Assume there is no rotational motion and loss of energy after the collision is negligible.)