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
mixer [17]
1 year ago
6

A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per

second. The height of the ball, in feet, can be represented by the function shown where t is the time, in seconds, since the ball was thrown. Rewrite the function in the form that would be best used to identify the maximum height of the ball and find Approximately when the object lands on the ground when rounded to the nearest tenth.

Mathematics
1 answer:
pishuonlain [190]1 year ago
3 0

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

y=a(t-h)^2+k

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

y=ax^2+bx+c

then the x-coordinate of the vertex is

h=-\frac{b}{2a}

Now in our case b = 32 and a = -16; therefore,

h=\frac{-32}{2(16)}=1

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

k=-16(1)+32(1)+96=112

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

h(t)=a(t-1)^2+112

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

h(0)=-16(0)^2+32(0)+96=96

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

96=a(0-1)^2+11296=a+112

subtracting 112 from both sides gives

a=-16

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

h(t)=0.

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

-16\left(t-1\right)^2+112=0

Now subtracting 112 from both sides gives

-16(t-1)^2=-112

Dividing both sides by -16 gives

(t-1)^2=\frac{-112}{-16}(t-1)^2=7

taking the square root of both sides gives

t-1=\pm\sqrt{7}

adding 1 to both sides gives

t=\pm\sqrt{7}+1

Hence, the two solutions we get are

t=\sqrt{7}+1=3.6t=-\sqrt{7}+1=-1.6

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

You might be interested in
In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
kirill115 [55]

Answer:

17

Step-by-step explanation:

55-15-18-5=17

8 0
3 years ago
Read 2 more answers
I may have alreadu asked this but...help !
Nataly_w [17]
The first price is 18.934 and the second is 25.929 but I’m not sure about the third
3 0
3 years ago
How do i find f(-1)?
jonny [76]
F(-1) is the inverses of an equation so plug in y for x.
4 0
2 years ago
The top box has a length of 6 yards
cricket20 [7]

Answer:

42 yd²

Step-by-step explanation:

Area of a rectangle = width x length

lateral surface area is the area of the sides only

So the difference between the total surface area and the lateral surface area would be the surface area of the ceiling and floor (top and bottom).

area of floor and ceiling = 2(3.5 x 6) = 42 yd²

Or, we can calculate the total surface area and lateral surface area, then find the difference:

total surface area = 2(3.5 x 4.2) + 2(4.2 x 6) + 2(3.5 x 6) = 121.8 yd²

lateral surface area = 2(3.5 x 4.2) + 2(4.2 x 6) = 79.8 yd²

difference = 121.8 - 79.8 = 42 yd²

6 0
2 years ago
Which expression is equivalent to 63?<br> 0 6х3<br> О 6х6х6<br> О 6х6х6х6<br> О 3х3х3х3х3х3
Illusion [34]
The last one with the 6 3s
3 0
3 years ago
Other questions:
  • Tilly the dog barks every 9 seconds.
    9·2 answers
  • Find the quotient 7.980 divided by 0.19
    15·1 answer
  • Rewrite the following equation in standard form. y=4x+10
    13·1 answer
  • 13. Three weeks ago John bought stock at 49'/s; today the stock is valued at 49'/s. We could say the stock is performing at whic
    5·2 answers
  • Y and x have a proportional relationship, and y = 25 when x = 60.
    9·2 answers
  • The sum of (-12) and (5) is<br><br> (A) 6 (B) 8 (C) -7
    15·2 answers
  • PLEASE HELPPP!!!<br> explain how you know!
    5·1 answer
  • Which ordered pair is a solution to the system of linear equations?
    14·2 answers
  • The product of p and 6
    15·1 answer
  • Suppose that electricity for the Lopez family toaster cost Ghc8.00 per hour. How much money will the Lopez family pay per year i
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!