Classical Mechanics

# 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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