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1D Dynamics - Problem Solving


A ball starts to free-fall from a height of \(5.4\text{ m}.\) At the point when the ball is \(3.3\text{ m}\) above the ground, what is the approximate velocity of the ball?

The gravitational acceleration on earth is about \(9.8\text{ m/s}^2.\)

A 100-gram cylindrical glass is attached to a string that hangs from the ceiling. Then the glass which has a cross-sectional radius of 4 cm and a height of 15 cm is slowly filled with water. If the string breaks when the glass is \(\frac23\) full, what is the maximum tension in Newtons that the string can support?

Details and Assumptions:

  • The acceleration of gravity is \(-9.8\text{ m/s}^2.\)
  • The density of water is \(1\text{ g/cm}^3.\)

An object is vertically thrown to the sky from the ground with an initial velocity of \(7.2\text{ m/s}.\) Approximately how long does it take in seconds for the object to fall back to the ground?

The acceleration of gravity on earth is about \(g=9.8\text{ m/s}^2.\)

An airplane is taxiing on a straight runway for takeoff with a constant acceleration. At time \(t=11.5\text{ s}\) the plane has a velocity of \(127\text{ km/h}, \) and at time \(t=15.5\text{ s}\) the plane's velocity is \(152\text{ km/h}.\) Find the approximate acceleration of the plane.

An advanced humanoid robot is running a marathon with a constant velocity of \(7.7\text{ m/s}.\) Near the finish line, it starts to accelerate with a constant acceleration of \(0.70\text{ m/s}^2\) for \(74 \text{ s}\) until it reaches the finish line. What was the robot's approximate distance from the finish line when it started to accelerate?


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