1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
3241004551 [841]
3 years ago
9

Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the ques

tions below. Show all your work for full credit. Use the correct units with your answers

Mathematics
1 answer:
Korvikt [17]3 years ago
5 0

Answer:

Step-by-step explanation:

From what I understand about parabolic motion in the English system, the equation for flight is

s(t)=-16t^2+v_{0}t+h_{0}

where v_{0}t is the initial upwards velocity and

h_{0} is the initial height from which the object was launched.  Filling in that equation with those values gives you

s(t)=-16t^2+64t+3.  That's a.

In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function.  The absolute max is the heighest that the ball will go.  Completing the square is the way to solve this.  Begin by setting the equation equal to 0, the moving the 3 over by subtraction:

-16t^2+64t=-3

Now factor out the -16 since the leading coefficient HAS to be a positive 1:

-16(t^2-4t)=-3

Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:

-16(t^2-4t+4)=-3

BUT since you added in a 4*-16 on the left you have to add it in on the right:

-16t^2(t^2-4t+4)=-3-64

which simplifies to

-16(t-2)^2=-67

Now bring the 67 over by addition and you have your vertex:

s(t)=-16(t-2)^2+67.

The vertex is (2, 67).  The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.

How long it will be in the air is found by factoring to find the zeros.  These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046

So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at

x = 4.05 seconds.  Which makes sense if you know anything about parabolic motion and physics.  The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark.  Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds.  And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters).  Sorry it's so long, but it's not a question that can be answered with just a few sentences.

You might be interested in
I need some help plz
Dmitrij [34]
There is : 3 pencils
4 Bubble gums
2 sports cards
In each favor bag
4 0
3 years ago
Why is cube root of 9 equal to 9 to the one third power question mark
kozerog [31]

Answer:

3

just because

3 0
3 years ago
Read 2 more answers
How many feet are 10 yards?
Minchanka [31]
30feet are in 10yards
5 0
3 years ago
Read 2 more answers
The angle between 0 and 2 π in radians that is coterminal with the angle 62 9 π in radians is
Anestetic [448]
Ill  recomment on my thing right now with the answer let me just go read up on how to do this 
3 0
3 years ago
If my brother eats 6 1/2 cupcakes in the morning, and comes back at night for 7 1/2 MORE cupcakes, how many did he eat in total.
ikadub [295]

Answer:

14

Step-by-step explanation:

6 1/2+7 1/2= 14

3 0
2 years ago
Read 2 more answers
Other questions:
  • Solve for x: 2x^5/3-22=464 a) x = 28 b) x = 27 c) x = ±27 d) x = ±28
    9·1 answer
  • How many weeks are in 68 days
    8·1 answer
  • Help<br> Which expression is the completely factored form of 27x^3+y^6?<br> In parenthesis form
    5·1 answer
  • 2. What is the diameter of the circle below?
    5·2 answers
  • Pls help it's confusing​
    6·2 answers
  • Write the equation of a line that is parallel to y = 1/2 x + 5
    15·1 answer
  • Lim x-&gt;pi/3 ((2cosx-1)/(tan^2x-3))
    7·1 answer
  • Find the weight in pounds of a 140-kilogram person. Round to the nearest hundredth​
    7·1 answer
  • <img src="https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B2%7Dx%20%2B%209" id="TexFormula1" title="y = - \frac{1}
    13·1 answer
  • A coffee shop sells five different flavors of coffee. They want to compare how much of each is sold on Saturday morning. Which g
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!