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:

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 \(g = 10~\text{m/s}^2)\)$$

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 \(v\)?