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Question 1

A ball is thrown off a low cliff to the beach below. It is thrown into the air with an initial upward velocity of 5 meters per second. The following graph models its height above sea level in meters over time in seconds.

The graph image shows a dot at (0,10), sloping up to (0.5,11), and then going back down, hitting (2,0). The Y coordinate represents Height Above Sea Level (in Meters), and the X coordinate represents time (in seconds).

1 answer

To analyze the motion of the ball based on the provided description of the graph, we can extract several key pieces of information.

  1. Initial Height: The ball starts at a height of 10 meters above sea level at time \(t = 0\).

  2. Initial Velocity: The ball is thrown with an initial upward velocity of 5 meters per second, indicating that it will rise initially before beginning to fall.

  3. Graph Behavior: The graph shows that the height increases from 10 meters to 11 meters at \(t = 0.5\) seconds (indicating upward motion). After \(t = 0.5\) seconds, the height begins to decrease, which indicates the ball is reaching its maximum height and then starting to fall back down. The ball reaches a height of 0 meters (the beach) at \(t = 2\) seconds.

From this, we can deduce:

  • The maximum height is reached between \(t = 0.5\) and \(t = 2\) seconds.
  • The ball takes a total of 2 seconds to hit the beach, starting from an initial height of 10 meters and rising to a peak before falling back down.

Questions You Might Consider Asking

  • What is the maximum height reached by the ball?
  • What are the equations of motion for the ball?
  • How long does it take to reach the maximum height?
  • Can we determine the ball's acceleration?

Potential Calculations and Concepts

  • The vertex of the motion can be calculated using the initial velocity and time to determine the maximum height.
  • The ball's trajectory follows a parabolic path due to the effects of gravity, which we can quantify if we use the kinematic equations of motion.
  • By analyzing the graph or using physics principles, we could calculate the displacement, velocity, and acceleration.

If you have specific questions or calculations you would like me to perform regarding this situation, please let me know!