SOLUTION: American astronauts working on the space station toss a ball into the air. the height of the ball is represented by the quadratic y=-2.7x^2+13.5x+14, where x represents the number
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Question 372144: American astronauts working on the space station toss a ball into the air. the height of the ball is represented by the quadratic y=-2.7x^2+13.5x+14, where x represents the number of seconds since the ball was thrown and y represents the height of the ball in feet.
a) to the nearest hundredth of a second, after how much time does the ball hit the ground?
b) to the nearest tenth of a foot, what is the greatest height the ball achieves? Answer by solver91311(24713) (Show Source):
To answer the questions precisely as you posed them would require knowing the distance from the surface of the earth to the space station plus a bunch of data and physics about the orbital decay of a ball left in earth orbit. This is in view of the fact that "the ground" is back on earth.
On the other hand, if what you really meant to ask is:
a) to the nearest hundredth of a second, after how much time does the ball hit the deck of the space station above which the ball was thrown?
b) to the nearest tenth of a foot, what is the greatest height above the deck of the space station the ball achieves?
Then for part a: Set the quadratic equal to zero and solve for the positive root. And for part b: Evaluate the function at the x-coordinate of the vertex of the parabola. The x-coordinate of the vertex of is found by calculating . Evaluating the function at that point means calculating and then rounding appropriately, of course.
John
My calculator said it, I believe it, that settles it
