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Classical Mechanics

# 2D Kinematics: Level 2-4 Challenges

A stone is thrown from the surface of Earth, where the acceleration due to gravity is $$9.8 \text{ m/s}^2.$$ The stone travels along a parabolic trajectory.

If the same stone is thrown exactly the same way from the surface of Mars, where the acceleration due to gravity is $$3.7 \text{ m/s}^2,$$ then the Martian trajectory is $$\text{__________}$$ the trajectory on Earth,

Which of the following statements are true for a basketball that is projected diagonally upwards (air resistance cannot be ignored)?

a. The basketball's kinetic energy is zero at the highest point of its motion.

b. The basketball’s average kinetic energy is smaller when traveling upwards than downwards.

c. The time taken for the basketball to travel upwards is less than the time taken to travel downward.

d. The horizontal distance traveled when the basketball is moving upwards is equal to the horizontal distance traveled when the basketball is moving downwards.

A little boy swings back and forth on the playground. At the highest point in his swing his speed is zero, and at his lowest point his speed is greatest.

Where in the trajectory will his acceleration be zero?

###### Caution: The acceleration is the rate of change of velocity and not the rate of change of speed.

A bead slides from rest down a wire that's bent into a helix, which can be parametrized in the following way: $\begin{cases} x = \cos(\theta) \\ y = \sin(\theta) \\ z = \theta. \end{cases}$ Find the magnitude of the bead's vertical acceleration.


Assumptions: The bead slides without friction and there is a uniform, gravitational field $$-g\,\hat{\mathbf{z}}.$$

What should be the height $$H$$ in meters so that the ball of mass $$\SI{1}{\kilo\gram}$$ reaches the point $$A?$$

Take $$g=\SI[per-mode=symbol]{10}{\meter\per\second\squared}.$$

• There is no friction in this system.
• The ball is not rolling it is sliding.
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