Questions: Projectile Motion Review I. Motion Parameters Indicate which direction (x or y) corresponds to the motion parameter 1. Time graph of (x, y) is a diagonal line 2. Time graph of (x, y) is a curve 3. Time graph of (vx, vy) is a straight diagonal line 4. Time graph of (vx, vy) is a straight horizontal line 5. Time graph of (ax, ay) is a straight horizontal line at 0 6. Time graph of (ax, ay) is a straight horizontal line at -10 II. Horizontal Launch: A marble rolls off of a table and lands 0.3 seconds later at an x-distance of 4 m. 7. Calculate the Vx 8. Calculate table height 9. Draw a labelled vector diagram for the landing. 10. Calculate the angle of impact. III. Angular Launch: A ball is kicked at 15 m/s at angle of 10 degrees above the ground. 11. Draw a labelled vector diagram for the kick. 12-13. Calculate Vxi and Vyi. 14. Calculate hmax 15. Calculate maximum range

Projectile Motion Review I. Motion Parameters Indicate which direction (x or y) corresponds to the motion parameter 1. Time graph of (x, y) is a diagonal line 2. Time graph of (x, y) is a curve 3. Time graph of (vx, vy) is a straight diagonal line 4. Time graph of (vx, vy) is a straight horizontal line 5. Time graph of (ax, ay) is a straight horizontal line at 0 6. Time graph of (ax, ay) is a straight horizontal line at -10 II. Horizontal Launch: A marble rolls off of a table and lands 0.3 seconds later at an x-distance of 4 m. 7. Calculate the Vx 8. Calculate table height 9. Draw a labelled vector diagram for the landing. 10. Calculate the angle of impact. III. Angular Launch: A ball is kicked at 15 m/s at angle of 10 degrees above the ground. 11. Draw a labelled vector diagram for the kick. 12-13. Calculate Vxi and Vyi. 14. Calculate hmax 15. Calculate maximum range
Transcript text: Projectile Motion Review I. Motion Parameters Indicate which direction ( $x$ or y ) corresponds to the motion parameter 1. Time graph of $(x, y)$ is a diagonal line 2. Time graph of $(x, y)$ is a curve 3. Time graph of $(v x, v y)$ is a straight diagonal line 4. Time graph of $(v x, v y)$ is a straight horizontal line 5. Time graph of ( $a x, a y$ ) is a straight horizontal line at 0 6. Time graph of (ax, ay 0 is a straight horizontal line at -10 II. Horizontal Launch: A marble rolls off of a table and lands 0.3 seconds later at an $x$-distance of 4 m . 7. Calculate the Vx 8. Calculate table height 9. Draw a labelled vector diagram for the landing. 10. Calculate the angle of impact. III. Angular Launch: A ball is kicked at $15 \mathrm{~m} / \mathrm{s}$ at angle of 10 degrees above the ground. 11. Draw a labelled vector diagram for the kick. 12-13. Calculate Vxi and Vyi. 14. Calculate hmax 15. Calculate maximum range
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Solution

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Solution Steps

Step 1: Determine the Direction for Motion Parameters

  1. Time graph of \((x, y)\) is a diagonal line: This indicates a linear relationship between time and position, which is typical for uniform motion in the \(x\)-direction. Therefore, the direction is \(x\).

  2. Time graph of \((x, y)\) is a curve: A curved graph suggests acceleration, which is characteristic of motion in the \(y\)-direction due to gravity. Therefore, the direction is \(y\).

  3. Time graph of \((v_x, v_y)\) is a straight diagonal line: A diagonal line in a velocity-time graph indicates constant acceleration. Since horizontal motion (\(x\)) is typically constant velocity in projectile motion, this suggests the \(y\)-direction where acceleration due to gravity acts. Therefore, the direction is \(y\).

Step 2: Calculate the Horizontal Velocity \(V_x\)

For a horizontal launch, the horizontal velocity \(V_x\) can be calculated using the formula:

\[ V_x = \frac{\text{horizontal distance}}{\text{time}} \]

Given:

  • Horizontal distance = 4 m
  • Time = 0.3 s

\[ V_x = \frac{4 \, \text{m}}{0.3 \, \text{s}} = 13.3333 \, \text{m/s} \]

Step 3: Calculate the Table Height

The table height can be calculated using the formula for vertical motion under gravity:

\[ y = \frac{1}{2} g t^2 \]

Where:

  • \(g = 9.81 \, \text{m/s}^2\) (acceleration due to gravity)
  • \(t = 0.3 \, \text{s}\)

\[ y = \frac{1}{2} \times 9.81 \, \text{m/s}^2 \times (0.3 \, \text{s})^2 = 0.44145 \, \text{m} \]

Final Answer

  1. \((x, y)\) is a diagonal line: \(\boxed{x}\)
  2. \((x, y)\) is a curve: \(\boxed{y}\)
  3. \((v_x, v_y)\) is a straight diagonal line: \(\boxed{y}\)
  4. Calculate \(V_x\): \(\boxed{13.33 \, \text{m/s}}\)
  5. Calculate table height: \(\boxed{0.4415 \, \text{m}}\)
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