$A$ constant force $\vec{F} = 3\hat{i} - 2\hat{j} - \hat{k} \text{ N}$ causes a displacement $\vec{r} = 2\hat{i} - 3\hat{j} - 3\hat{k} \text{ m}$ in $2 \text{ s}$. The work done and the power are respectively:

Water falls from a $40\,m$ high dam at the rate of $9 \times 10^{4}\,kg$ per hour. Fifty percent of the gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy, the number of $100\,W$ lamps that can be lit is (Take $g = 10\,m/s^2$)

$A$ ball of mass $2m$ is moving with velocity $v$ on a smooth surface and collides elastically head-on with another ball of mass $m$ which is at rest. If the ball of mass $m$ reaches up to the top of a frictionless elevated plane of height $h$,then the velocity $v$ of the heavy ball must be

$A$ bullet of mass $25 \,g$ moving horizontally at a speed of $250 \,m/s$ is fired into a wooden block of mass $1 \,kg$ suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of $20 \,cm$, find the speed of the bullet as it emerges from the block. (Take $g = 10 \,m/s^2$) (in $\,m/s$)

$A$ particle of mass $m$ moving eastward with a speed $v$ collides with another particle of same mass moving northward with same speed $v$. The two particles coalesce after collision. The new particle of mass $2m$ will move in north-east direction with a speed (in $m/s$) of:

$A$ box of mass $3 \,kg$ moves on a horizontal frictionless table and collides with another box of mass $3 \,kg$ initially at rest on the edge of the table at height $1 \,m$. The speed of the moving box just before the collision is $4 \,m/s$. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume, acceleration due to gravity, $g=10 \,m/s^2$) (in $\,J$)