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Duffer McGee stood on a hill and used a nine iron to hit a golf ball that reached a maximum height of 172 feet and stayed in the air for 6.1 seconds before it touched the ground. Pretty good for a Duffer. Mars has a gravity of approximately 12 feet per second squared compared to Earth's 32 feet per second squared. NASA did a simulation to try to determine how high the golf ball would fly and how long it would stay in the air on Mars if it was hit at the same height, angle and velocity as Duffer's. The data below represent the results of that simulation: t 1 2 3 4 5 H(t) 128 201 262 311 348 Use the Quadratic Regression feature of your calculator to generate a mathematical model for this situation. Write the function below. Round each coefficient to the nearest whole number. H ( t ) = Based on your model how high is the hill from which the golf ball was hit?? The golf ball was hit from a hill feet high. Use your model to estimate how long the golf ball will take to reach its maximum height and what its maximum height will be. Round your answers to two decimal places. The golf ball will reach a maximum height of feet after seconds. Use your model to determine how long it will take for the golf ball to hit the surface of Mars. Round your answer to two decimal places. The golf ball will reach the surface of Mars after seconds.

Sagot :

Answer:

Estimated time to reach the surface of Mars: 6.03 secondsCG5c.aiTo find out how high the hill from which the golf ball was hit, we can use our model to evaluate H(0):

H(0) = 393

So the hill was approximately 393 feet tall.

To find out how long the golf ball will take to reach its maximum height and what its maximum height will be, we can use our model to find the vertex of the parabolic function. The vertex is given by (-b/(2a), f(-b/(2a))) which is (0, 128) in this case. This tells us the golf ball will reach its maximum height of2 / 30CG5c.aiThe mathematical model generated using the Quadratic Regression feature of the calculator is:

H(t) = 0.057t^2 - 0.13t + 12.8

Therefore, the hill from which the golf ball was hit is 128 feet high.

Using the model, the golf ball will reach a maximum height of 311 feet after 3.59 seconds and will take 3.00 seconds to reach this maximum.

Finally, it will take 0.82 seconds for the golf ball to hit the surface of Mars.

Step-by-step explanation:

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