Two stones are thrown up simultaneously from the edge of a cliff \(240~\text{m}\) high with an initial speed of \(10~\text{m/s}\) and \(40~\text{m/s}\) respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take
\(g= 10~\text{m/s}^2\))
(The figures are schematic and not drawn to scale)

1. 2.
3. 4.
Subtopic:  Relative Motion in One Dimension |
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A car is standing \(200~\text{m}\) behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \(2~\text{m/s}^2 \) and the car has acceleration \(4~\text{m/s}^2. \) The car will catch up with the bus after a time of:
1. \(\sqrt{120}~\text{s} \)
2. \(15~\text{s}\)
3. \(10\sqrt2~\text{s} \)
4. \(\sqrt{110}~\text{s} \)
Subtopic:  Relative Motion in One Dimension |
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Train \(\mathrm{A}\) and Train \(\mathrm{B}\) are running on parallel tracks in opposite directions with speeds of \(36~\text{km/h}\) and \(72~\text{km/h},\) respectively. A person is walking inside Train \(\mathrm{A}\) in the direction opposite to the train's motion with a speed of \(1.8~\text{km/h} .\) What is the speed of this person as observed from Train \(\mathrm{B}\)? (Assume the distance between the tracks is negligible.)

1. \(30.5\) m/s 2. \(29.5\) m/s
3. \(31.5\) m/s 4. \(28.5\) m/s
Subtopic:  Relative Motion in One Dimension |
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Two identical trains cross each other moving on parallel tracks, opposite in direction. Speed of one of the train is 70 km/hr and second train has a speed of 110 km/hr. If it takes 8 seconds for two trains to cross each other then length of trains is equal to 
1. 100 m 
2. 200 m 
3. 300 m 
4. 400 m
Subtopic:  Relative Motion in One Dimension |
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