When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -5t^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!
If your answer is negative, that means the ball already hit the ground, so choose a smaller value for time.
Think about a ball going up into the air, you might throw it or put in a cannon. If you throw a ball up into the air, it will not end up being 800 meters in the air if it leaves your hand at 5 meters. Therefore, you would need to adjust your initial velocity. You may want to research initial velocity (speed) to figure out what seems reasonable! (ex. Your 5 year old cannot throw a ball into the air with an initial velocity of 300 meters/sec) !
Do NOT use the same values for “v” and “k” as another student in the class.
They will not give the answer, you have to submit an answer, and then ask them They cannot do the assignments for you... it happened with me.
Scenario:
Let's consider a scenario where a ball is thrown up into the air from the top of a building. The initial velocity of the ball is 20 meters/sec, and the initial height (k) of the ball from the ground is 30 meters.
1. Inserting the values into the formula:
The equation becomes S = -5t^2 + 20t + 30.
2. Calculating the height of the ball at two different values of time (t):
a. Let's calculate the height at t = 2 seconds:
S = -5(2)^2 + 20(2) + 30
S = -5(4) + 40 + 30
S = -20 + 40 + 30
S = 50 meters
b. Now, let's calculate the height at t = 4 seconds:
S = -5(4)^2 + 20(4) + 30
S = -5(16) + 80 + 30
S = -80 + 80 + 30
S = 30 meters
3. Summary of results:
The height of the ball at t = 2 seconds is 50 meters, and at t = 4 seconds, the height is 30 meters. These values represent the vertical position of the ball above the ground at different points in time.
In the context of the original problem, the ball starts its motion from the top of a building (30 meters above the ground) with an initial velocity of 20 meters/sec. As time progresses, the ball follows a parabolic path. At t = 2 seconds, the ball reaches a maximum height of 50 meters above its starting point. After that, the ball starts descending, and at t = 4 seconds, it is at a height of 30 meters above the ground.
Note: The values of "v" and "k" can be adjusted according to different scenarios, but they must be realistic and logical in relation to the context and physics of the problem.