SOLUTION: I was given the word problem: While Darnell is grounded his friend Jack brings him a video game. Darnell stands at his bedroom window, and Jack stands directly below the window. I

Question 702392: I was given the word problem:
While Darnell is grounded his friend Jack brings him a video game. Darnell stands at his bedroom window, and Jack stands directly below the window. If Jack tosses a game cartridge to Darnell with an initial velocity of 35 feet per second, an equation for the height h feet of the cartridge after t seconds is h=-16t^2+35t+5.
a. If the window is 25 feet above the ground, will Darnell have 0, 1, or 2 chances to catch the video game?
b. If Darnell is unable to catch the video game, when will it hit the ground?
Can you please help, I'm lost.
Thank you!

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If Jack tosses a game cartridge to Darnell with an initial velocity of 35 feet per second, an equation for the height h feet of the cartridge after t seconds is h=-16t^2+35t+5.
a. If the window is 25 feet above the ground, will Darnell have 0, 1, or 2 chances to catch the video game?
Solve: -16t^2+35t+5 = 25
----
-16t^2 + 35t - 20 = 0
b^2 -4ac = 35^2 - 4(-17)(-20) = -135
---
So there are no Real Number solutions.
Darnell will have 0 chances to catch the ball.
------------------------------------------------------
b. If Darnell is unable to catch the video game, when will it hit the ground?
Solve -16t^2 + 35t + 5 = 0
t = 2.322 seconds
====================
Cheers,
Stan H.
====================

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The height function is a quadratic with a negative lead coefficient. That means the graph opens downward and the vertex is a maximum. Divide the opposite of 1st degree coefficient by twice the lead coefficient to find the -coordinate of the vertex. Then evaluate the function at that -value to find the maximum height. If the maximum height is less than 25, 0 chances. If the maximum height is exactly 25 feet, 1 chance. If the maximum is more than 25, 2 chances (one on the way up, the other on the way down)

For the other part, remember that the ground is zero height. Set the function equal to zero and solve the quadratic equation. Discard the negative root -- you don't care what happened before the guy on the ground threw the thing, do you?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

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