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
Algebra.Com
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): You can put this solution on YOUR website!
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 \ =\ ax^2\ +\ bx +\ c)
is found by calculating 
. Evaluating the function at that point means calculating \ =\ a\left(\frac{-b}{2a}\right)^2\ +\ b\left(\frac{-b}{2a}\right) +\ c)
and then rounding appropriately, of course.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
.American astronauts working on a space station on the moon toss a ball into the air. The (answered by Boreal)
If a juggler can toss a ball into the air with a velocity of 64ft/sec from a height of 6... (answered by Earlsdon,Edwin McCravy)
Tom throws a ball into the air. The ball travels on a parabolic path represented by the... (answered by josmiceli)
Tom throws a ball into the air. The ball travels on a parabolic path represented by the... (answered by Fombitz)
Tom throws a ball into the air. The ball travels on a parabolic path represented by the... (answered by jorel1380)
Tom throws a ball into the air. The ball travels along a parabolic path represented by... (answered by lwsshak3)
You are hitting baseballs. When tossing the ball into the air, your hand is 5
feet above (answered by Edwin McCravy)
The height, y, of a ball tossed into the air can be represented by the equation {{{ y=... (answered by KMST,lwsshak3)
A ball is thrown straight up into the air. The approximate height h of the ball after t... (answered by stanbon)
