Math Problem Statement
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
This is the maximum height reached by the projectile. It can be calculated using: where:
- is the initial velocity,
- is the launch angle,
- is the acceleration due to gravity (usually ).
2. Jarak ke Titik Tertinggi
This is the horizontal distance when the projectile reaches its maximum height. It can be found using:
3. Waktu Tempuh ke Titik Tertinggi
The time it takes to reach the maximum height is:
4. Jarak ke Titik Terjauh (Range)
The range of the projectile (total horizontal distance traveled) can be calculated using:
5. Waktu Tempuh ke Titik Terjauh
The total time of flight is:
Steps to Fill the Table:
You need to plug in the given values for , , and calculate the results for each row using the formulas listed above.
Example for the first row:
Using the formulas, you can calculate , , , , and .
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:
- Would you like a detailed example for a specific row calculation?
- Do you need help with the trigonometric calculations for ?
- Should I explain how the formula changes if there is an initial height ?
- Would you like to review how air resistance is ignored in these calculations?
- 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
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