A steel ball is dropped from the roof of a building. A man standing in front of a $1 \mathrm{m}$ high window in the building notes that the ball takes $0.1 \mathrm{s}$ to the fall from the top to the bottom of the window. The ball continues to fall and strikes the ground. On striking the ground, the ball gets rebounded with the same speed with which it hits the ground. If the ball reappears at the bottom of the window $2 \mathrm{s}$ after passing the bottom of the window on the way down, find the height of the building.

The velocity-time graph for the vertical component of the velocity of an object thrown upward from the ground which reaches the roof of a building is shown in the figure. If the height of the building is $h \mathrm{meter}$. Find $\frac{h}{5}$.

Two balls are dropped from the top of a cliff at a time interval $∆t=2 \mathrm{s}$. The first ball hits the ground, rebounds elastically (essentially reversing direction instantly without losing speed) and collides with the second ball at height $h=55 \mathrm{m}$ above the ground. How high is the top of the cliff (in $\mathrm{m}$)?

A particle has an initial velocity $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and an acceleration of $0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}$. Its speed after $10 \mathrm{s}$ is,