Question 1108742: I have a test next week and need help working out and solving
a problem. If you could please help me with the steps that would be great!
James Bond stands on top of a 240-foot building and throws a film canister
upward to a fellow agent in a helicopter 16ft above the building. The height
of the film canister above the ground t seconds later given by the formula
H(t) = -16t^2 +32t + 240, where is h is in feet?
A. If the film canister reaches the agent in the helicopter at its
highest point, how long will it take the film canister to reach the agent?
B. If the film canister is not caught by the agent in the helicopter and
falls to the ground, how long will it take to hit the ground? Solve by
factoring.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
Sure. I will do it in two steps.
At the first step, I send you the list of my lessons in this site related to similar problems.
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
- Problem on a ball thrown vertically up from the top of a tower
- Problem on a toy rocket launched vertically up from a tall platform
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
========================
At the second step, I will show you how to solve your problem.
A. If the film canister reaches the agent in the helicopter at its highest point, how long will it take the film canister to reach the agent?
The question is: for how long the canister will reach its highest point ?
It is about at what value of "t" the quadratic form H(t) = -16t^2 +32t + 240 will reach its maximum ?
From the general theory, it will happen at t = "  ", refering to the general form q(x) = ax^2 + bx + c.
In your case it will happen at t =  = 1 second.
So, question A is just answered.
B. If the film canister is not caught by the agent in the helicopter and falls to the ground, how long will it take to hit the ground? Solve by factoring
This event will happen when H(t) = 0, which is
-16^t^2 + 32t + 240 = 0.
As they ask us, I will solve this quadratic equation by factoring the left side polynomial
-16(t-5)*(t+3) = 0.
It gives you the UNIQUE positive root t= 5, which means that the canister will reach the ground in 5 seconds after it was thrown upward.
Solved.
---------------
The addition portion of the lessons on finding the maximum/minimum of a quadratic function is this:
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
Again, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! James Bond stands on top of a 240-foot building and throws a film canister
upward to a fellow agent in a helicopter 16ft above the building. The height
of the film canister above the ground t seconds later given by the formula
H(t) = -16t^2 +32t + 240, where is h is in feet?
A. If the film canister reaches the agent in the helicopter at its
highest point, how long will it take the film canister to reach the agent?
B. If the film canister is not caught by the agent in the helicopter and
falls to the ground, how long will it take to hit the ground? Solve by
factoring.
H(t) = -16tē + 32t + 240
The highest point is the vertex of the parabola
We use the vertex formula, which is:
for a = -16, b = 32, and c = 240
So when t=1 second, it reaches its maximum height of
256 feet, which is 16 feet above the 240-foot building.
(We did not need that information).
Answer: it takes him 1 second.
--------------
B. If the film canister is not caught by the agent
in the helicopter and falls to the ground, how long will
it take to hit the ground? Solve by factoring
The ground is 0 feet from the ground.
So we substitute 0 for H(t) and solve for t:
H(t) = -16tē + 32t + 240
0 = -16tē + 32t + 240
Divide through by -16
0 = tē - 2t - 15
Factor:
0 = (t - 5)(t + 3)
t - 5 = 0; t + 3 = 0
t = 5; t = -3 (time can't be negative,
so the only solution is t = 5 seconds.
Edwin
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