When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -10t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in meters/sec and “k” is the initial height in meters (as if you were on top of a tower or building).
Make up a scenario where a ball is thrown, shot, etc. into the air. You can choose any initial velocity (in meters/sec) and any initial height (in meters) of the ball, but include them in your written scenario. The ball can leave your hand, the top of a building, etc. so you can use many different values for the initial height.
1. Insert the chosen values for “v” and “k” into the formula listed above.
2. Use the formula to find the height of the ball at any two values of time, t, in seconds that you want. Show your calculations and put units on your final answer!
3. Provide a written summary of your results explaining them in the context of the original problem.
Please make sure that your answers make sense!
S= -10t^2 + v*t + k
I think this should be approximately
S= -4.9t^2 + v*t + k
if height is in meters on our earth.
In general
h = Hinitial + Vi t + (1/2) g t^2
where g is about 9.8 meters/second^2
on earth surface.
Part 1: Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer.
Cite your sources using APA style.
Part 2:
An application of a rational function is T = (AB)/(A+B), which gives the time, T, it takes for two workers to complete a particular task where A & B represent the time it would take for each individual worker to complete the identical task.
Estimate how long it takes you to complete a task of your choice (house cleaning, mowing, etc.) in a given week. Suppose that Joe is slower than you at the given task and takes three times as long as you do. If you work together, how long would it take you to complete the task?
Include the type of job, the time it takes you and Joe individually to complete the job, and the calculations needed to show how long it would take to complete the job if you worked together. Include units with your answer.
Scenario: A ball is thrown from the top of a building with an initial velocity of 20 meters per second and an initial height of 50 meters.
1. Inserting the chosen values for "v" and "k" into the equation S = -10t^2 + vt + k:
S = -10t^2 + 20t + 50
2. Finding the height of the ball at two different values of time, t:
a) Let's find the height of the ball after 3 seconds:
- Plug in t = 3 into the equation:
S = -10(3)^2 + 20(3) + 50
S = -90 + 60 + 50
S = 20 meters
b) Now, let's find the height of the ball after 5 seconds:
- Plug in t = 5 into the equation:
S = -10(5)^2 + 20(5) + 50
S = -250 + 100 + 50
S = -100 meters
3. Summary of results:
a) After 3 seconds, the ball reaches a height of 20 meters.
b) After 5 seconds, the ball has reached a height of -100 meters.
In the context of the problem, a positive height indicates that the ball is above the initial height (in this case, the top of the building), while a negative height indicates that the ball has fallen below the initial height.
So, after 3 seconds, the ball has reached a height of 20 meters above the top of the building. After 5 seconds, the ball has fallen below the top of the building by 100 meters.