A particle is projected vertically from the ground takes time $t_1=1 \mathrm{s}$ up to point $A$, $t_2=3 \mathrm{s}$ from point $A$ to $B$, and time $t_3=4 \mathrm{s}$ from point $B$ to the highest point. Find the height of the middle point of $A$ and $B$ from the ground.

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,