Math Problem Statement

Fill in the table based on your experimental results for projectile motion, including calculations for the highest point (maximum height), the range, and the time of flight.

Solution

From the image you uploaded, it appears that you are working on projectile motion problems and are tasked with filling out a table based on the results of an experiment. The table involves calculating values related to the highest point (the peak) and the farthest point of the projectile motion, such as maximum height, range, and time of flight.

To summarize the steps and formulas needed to calculate the required values:

1. Titik Tertinggi SyS_{y}

This is the maximum height reached by the projectile. It can be calculated using: Sy=v02sin2(θ)2gS_{y} = \frac{v_0^2 \sin^2(\theta)}{2g} where:

  • v0v_0 is the initial velocity,
  • θ\theta is the launch angle,
  • gg is the acceleration due to gravity (usually 9.8m/s29.8 \, \text{m/s}^2).

2. Jarak ke Titik Tertinggi SxtertinggiS_{x_{\text{tertinggi}}}

This is the horizontal distance when the projectile reaches its maximum height. It can be found using: Sxtertinggi=v02sin(2θ)2gS_{x_{\text{tertinggi}}} = \frac{v_0^2 \sin(2\theta)}{2g}

3. Waktu Tempuh ke Titik Tertinggi ttertinggit_{\text{tertinggi}}

The time it takes to reach the maximum height is: ttertinggi=v0sin(θ)gt_{\text{tertinggi}} = \frac{v_0 \sin(\theta)}{g}

4. Jarak ke Titik Terjauh SxS_{x} (Range)

The range of the projectile (total horizontal distance traveled) can be calculated using: Sx=v02sin(2θ)gS_{x} = \frac{v_0^2 \sin(2\theta)}{g}

5. Waktu Tempuh ke Titik Terjauh tterjauht_{\text{terjauh}}

The total time of flight is: tterjauh=2v0sin(θ)gt_{\text{terjauh}} = \frac{2v_0 \sin(\theta)}{g}

Steps to Fill the Table:

You need to plug in the given values for v0v_0, θ\theta, and calculate the results for each row using the formulas listed above.

Example for the first row:

  • h=0h = 0
  • θ=30\theta = 30^\circ
  • v0=15m/sv_0 = 15 \, \text{m/s}

Using the formulas, you can calculate SyS_{y}, SxtertinggiS_{x_{\text{tertinggi}}}, ttertinggit_{\text{tertinggi}}, SxS_{x}, and tterjauht_{\text{terjauh}}.

Would you like me to calculate these for one of the rows to help you fill out the table? Let me know!

Follow-up questions:

  1. Would you like a detailed example for a specific row calculation?
  2. Do you need help with the trigonometric calculations for θ\theta?
  3. Should I explain how the formula changes if there is an initial height hh?
  4. Would you like to review how air resistance is ignored in these calculations?
  5. Do you need assistance with unit conversions or approximations?

Tip: Always keep your angle in radians when using scientific calculators unless they are set to degree mode.

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Kinematics
Trigonometry

Formulas

Maximum height (S_y) = (v_0^2 * sin^2(θ)) / (2 * g)
Horizontal distance to maximum height (S_x_tertinggi) = (v_0^2 * sin(2θ)) / (2 * g)
Time to maximum height (t_tertinggi) = (v_0 * sin(θ)) / g
Range (S_x) = (v_0^2 * sin(2θ)) / g
Total time of flight (t_terjauh) = (2 * v_0 * sin(θ)) / g

Theorems

Kinematic equations for projectile motion under gravity without air resistance

Suitable Grade Level

Grades 10-12