Library Assignment
When a ball is thrown up into the air, it makes the shape of a parabola. The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in ft/sec and “k” is the initial height in feet (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 feet/sec) and any initial height (in feet) 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.
Insert the chosen values for “v” and “k” into the formula listed above.
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!
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 feet in the air if it leaves your hand at 5 feet. 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 feet/sec) J
Do NOT use the same values for “v” and “k” as another student in the class.
So exactly what is your question. This assignment seems extraordinarily clear to me.
I would make a table
v k time1, time2 h1 h2
put in v, k that you choose, choose times1 and 2, then calculate h1 and h2 using the formulas.
Scenario:
A basketball player, standing at the top of a tower, decides to shoot a basketball into the air. The initial velocity of the ball is 25 ft/sec and the initial height of the tower is 50 feet.
Using the given equation S = -16t^2 + vt + k, we can substitute the values v = 25 ft/sec and k = 50 feet:
S = -16t^2 + 25t + 50
To find the height of the ball at two different times, let's use t = 2 seconds and t = 4 seconds.
1. For t = 2 seconds:
S = -16(2)^2 + 25(2) + 50
S = -64 + 50 + 50
S = 36 feet
Therefore, at t = 2 seconds, the height of the ball is 36 feet.
2. For t = 4 seconds:
S = -16(4)^2 + 25(4) + 50
S = -256 + 100 + 50
S = -106 feet
Since the calculated height is negative, it means the ball has already hit the ground before reaching a time of 4 seconds. Hence, we need to choose a smaller value for time.
Summary:
Based on the calculations, when the basketball is shot into the air with an initial velocity of 25 ft/sec and from a tower height of 50 feet, we find that the ball reaches a height of 36 feet at 2 seconds. This means that after being shot, the ball goes up, reaches a peak height of 36 feet, and then starts descending.