A projectile is fired from the ground with the x-coordinate horiz and the y-coordinate vertical (positive upwards). The angle the projectile 1 with the horizontal axis is 30 deg. Sketch on the axis below each compon the motion r(t) and y(t) as functions of time. Also, sketch the kinetic ener a function of time. Construct the graphs so that the time is aligned on all t: x coordinate oordinate + +

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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A projectile is fired from the ground with the x-coordinate horizontal and the y-coordinate vertical (positive upwards). The angle the projectile makes with the horizontal axis is 30 degrees. Sketch on the axes below each component of the motion \( x(t) \) and \( y(t) \) as functions of time. Also, sketch the kinetic energy as a function of time. Construct the graphs so that the time is aligned on all three.

**Graphs Explanation:**

1. **x-coordinate vs. time:**
   - The x-coordinate will change linearly with time as the projectile moves horizontally. This graph will show a positive slope starting from zero, indicating a constant horizontal velocity.

2. **y-coordinate vs. time:**
   - The y-coordinate graph will have a parabolic shape. It will start from zero, rise to a peak, and then fall back to zero, depicting the upward and downward motion of the projectile due to gravity.

3. **Kinetic energy vs. time:**
   - The kinetic energy graph will initially be positive, decrease to a minimum at the peak of the projectile's path, and then increase again as the projectile descends. This indicates that the kinetic energy is highest when the projectile is moving fastest.
Transcribed Image Text:A projectile is fired from the ground with the x-coordinate horizontal and the y-coordinate vertical (positive upwards). The angle the projectile makes with the horizontal axis is 30 degrees. Sketch on the axes below each component of the motion \( x(t) \) and \( y(t) \) as functions of time. Also, sketch the kinetic energy as a function of time. Construct the graphs so that the time is aligned on all three. **Graphs Explanation:** 1. **x-coordinate vs. time:** - The x-coordinate will change linearly with time as the projectile moves horizontally. This graph will show a positive slope starting from zero, indicating a constant horizontal velocity. 2. **y-coordinate vs. time:** - The y-coordinate graph will have a parabolic shape. It will start from zero, rise to a peak, and then fall back to zero, depicting the upward and downward motion of the projectile due to gravity. 3. **Kinetic energy vs. time:** - The kinetic energy graph will initially be positive, decrease to a minimum at the peak of the projectile's path, and then increase again as the projectile descends. This indicates that the kinetic energy is highest when the projectile is moving fastest.
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