A stone is thrown vertically downwards with an initial velocity of \(40\) m/s from the top of a building. If it reaches the ground with a velocity of \(60\) m/s, then the height of the building is: (Take \(g=10\) m/s²)
1. \(120\) m
2. \(140\) m
3. \(80\) m
4. \(100\) m

A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\frac{S_n}{S_{n +1}}\) is:
1. \(\frac{2n+1}{2n-1}\)
2. \(\frac{2n}{2n-1}\)
3. \(\frac{2n-1}{2n}\)
4. \(\frac{2n-1}{2n+1}\)

A ball is thrown vertically downwards with a velocity of \(20\) m/s from the top of a tower. It hits the ground after some time with the velocity of \(80\) m/s . The height of the tower is: (assuming $\mathrm{g}=10$ $\mathrm{m}/{\mathrm{s}}^2)$

A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)
1. \(15.5~\text{m/s}\)
2. \(14.5~\text{m/s}\)
3. \(4.5~\text{m/s}\) 
4. \(20~\text{m/s}\) 

A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:

A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after \(10\) s will be:

A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds, another ball is thrown downwards from the same platform with speed v. The two balls meet after 18 seconds. What is the value of v?