SOLUTION: challenge: William and Stephanie are playing a rather dangerous game of catch on the rooftops of skyscrapers in downtown Chicago. William is preparing to throw a tennis ball off t

Question 935429: challenge:
William and Stephanie are playing a rather dangerous game of catch on the rooftops of skyscrapers in downtown Chicago. William is preparing to throw a tennis ball off the roof of the John Hancock Center,1130 feet above street level Stephanie is waiting to catch the ball on the rooftop of the neighboring Water Tower Place,830 feet above street level. William throws the ball,which leaves his hand with an upward velocity of 46 feet per second, and travels in a parabolic path. Stephanie catches the ball exactly 6.0 seconds after it is thrown.
complete the following tasks:
1-Create a quadratic function describing the height of the ball above street level with respect to time t.
2- After how many seconds will the ball reach its maximum height above street level?
3- Find the maximum height of the ball above street level .Round to the nearest foot.
4- Stephanie uses a machine to launch the ball back up to William ,who catches it exactly 6.0 seconds after it is launched. What is the upward velocity in feet per second of the ball as it leaves the launcher? thank you so much.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
William is preparing to throw a tennis ball off the roof of the John Hancock Center,1130 feet above street level
Stephanie is waiting to catch the ball on the rooftop of the neighboring Water Tower Place,830 feet above street level.
William throws the ball,which leaves his hand with an upward velocity of 46 feet per second, and travels in a parabolic path.
Stephanie catches the ball exactly 6.0 seconds after it is thrown.
complete the following tasks:
1-Create a quadratic function describing the height of the ball above street level with respect to time t.
y = -16t^2 + 46t + 1130
Looks like this

green line at 830 ft, intersects at 6 sec
:
2- After how many seconds will the ball reach its maximum height above street level?
max height occurs at the axis of symmetry, x = -b/(2a)
t =
t = 1.4375 sec for max height
3- Find the maximum height of the ball above street level .Round to the nearest foot.
f(t) = height above street level
f(t) = -16(1.4375^2) 47(1.4375) + 1130
f(t) = -33.0625 + 66.125 + 1130
f(t) = 1163 ft above street level is max height
:
4- Stephanie uses a machine to launch the ball back up to William ,who catches it exactly 6.0 seconds after it is launched.
What is the upward velocity in feet per second of the ball as it leaves the launcher
let v = upward velocity
f(t) = 1130, t = 6 sec
-16(36) + 6v + 830 = 1130
-576 +6v + 830 = 1130
6v = 1130 - 830 + 576
6t = 836
v = 146 ft/sec
RELATED QUESTIONS
Nicola, Stephanie, Kathryn, and William, in that order, take turns at rolling a fair die... (answered by Fombitz)

I don't know what the upside down u means. Can you please help me? Thank you in advance!! (answered by richard1234)

You are playing Pokémon-go in Chicago. The number of Pokémon you see is inversely... (answered by solver91311)

You are playing Pokémon-go in Chicago. The number of Pokémon you see is inversely... (answered by Boreal)

Lauren is playing a game of chance. In order to win, she must draw a spade or a heart... (answered by mathsolverplus,greenestamps)

Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal (answered by ankor@dixie-net.com)

Stephanie and her friend, Paula, are waiting for a shuttle to take them to their... (answered by ankor@dixie-net.com)

Suppose a standard six-sided die is rolled and you receive $0.50 for every dot showing on (answered by richard1234)

In a TV game show, 4 prizes are hidden on a game board that contains 20 spaces. One... (answered by stanbon)