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

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

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- given the following annual demand, annual carring cost and ordering cost D = $50000 per year CO = 500 per order CH $0.25 per unit per year calculate: optimal