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
ivann1987 [24]
3 years ago
15

A waterfall has a height of 1200 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet p

er second. The​ height, h, of the pebble after t seconds is given by the equation -16t^2+24t+1200 . How long after the pebble is thrown will it hit the​ ground?
Mathematics
1 answer:
Gemiola [76]3 years ago
3 0

Answer: 9.44 seconds

Step-by-step explanation:

A movement equation in the vertical axis is usually written as follows:

p(t) = (-g/2)*t^2 + v0*t + p0

where:

g is the gravitational acceleration, in this case is 32 ft/s^2, then -g/2 = -16ft/s^2

v0 is the initial velocity, in this case, 24 ft/s

p0 is the initial height, in this case, 1200ft

Then, when p(t)  = 0ft will mean that the pebble will hit the ground, then we need to calculate:

p(t) = -16t^2+24t+1200  = 0

and find the value of t, this is a quadratic equation, then we can use the Bhaskara equation to find the two solutions, these are:

t = \frac{-24 +- \sqrt{24^2 - 4*(-16)*1200} }{2*-16} = \frac{-24 +- 278.2}{-32}

Then the two solutions are:

t = (-24  + 278.2)/-32 = -7.94 seconds (we can discard this one, because the negative time is not really defined)

t = (-24 - 278.2)/-32 = 9.44 seconds

Then the pebble needs 9.44 seconds to hit the ground

You might be interested in
How to solve x/3 + 4 = -2
r-ruslan [8.4K]

Answer:

x=−18

Step-by-step explanation:

Let's solve your equation step-by-step.

x

3

+4=−2

Step 1: Simplify both sides of the equation.

1

3

x+4=−2

Step 2: Subtract 4 from both sides.

1

3

x+4−4=−2−4

1

3

x=−6

Step 3: Multiply both sides by 3.

3*(

1

3

x)=(3)*(−6)

x=−18

5 0
2 years ago
Read 2 more answers
Hey can someone help me with this
ivanzaharov [21]

Step-by-step explanation:

The median is the middle number is an ordered set of data. In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position. If there is an odd number of observations, the median is the middle number

7 0
2 years ago
Which correctly places these plot events in order? 2, 5, 1, 3, 4 5, 1, 3, 4, 2 4, 2, 5, 1, 3 3, 4, 2, 5, 1.
Tema [17]

please add more information

6 0
2 years ago
Read 2 more answers
Find the slope of the line that passes through (-19, -33) and (47, 5)
Vera_Pavlovna [14]
Hello there! Slope is rise/run. The formula for finding slope is y2 - y1 / x2 - x1, where you subtract the first x and y-coordinates from the second x and y-coordinates. In other words, the order that the coordinates show up for this problem will be used in that order. For this case, here are the numbers that will be used for each.

y2: 5
y1 : -33
x2: 47
x1: -19

Let's plug it in to get 5 - (-33) / 47 - (-19). Now, let's subtract. Just by looking at the numbers, we will actually be adding the numbers, because when you add a negative number, you actually add. So 5 + 33 is 38. 47 + 19 is 66. 38/66 is 19/33 in simplest form. There. The slope of the line is 19/33.
8 0
3 years ago
What is the value of k if √10 * k + 3 = 5?
Fittoniya [83]

Answer:

See explanation

Step-by-step explanation:

We want to find the value of k in

\sqrt{10k}  + 3 = 5

We subtract 3 from both sides;

\sqrt{10k}  = 5 - 3

Simplify on the right;

\sqrt{10k}  = 2

Square both sides;

10k = 4

k = 0.4

If your equation in actually

\sqrt{10k + 3}  = 5

Square both sides:

10k + 3 = 25

10k = 22

k = 2.2

7 0
3 years ago
Other questions:
  • Using the parkland formula, calculate the hourly rate of fluid replacement with lactated ringerâs solution during the first 8 ho
    6·1 answer
  • Need this question answered correctly and FAST! PLEASE!
    5·1 answer
  • Ashlyn had some Barbie dolls. Joslyn has 78 barbies. Rounded to the nearest ten, together they have 140 Barbie dolls. How many d
    11·2 answers
  • When you combine equal groups you can
    12·1 answer
  • 9-5(4-2)<br> --------------<br> 3+5
    10·1 answer
  • Given: 1/3 x+y= 15.
    12·1 answer
  • The freezing point of a certain liquid is -7F . Another liquid freezes at -12F . What is the difference between the absolute val
    10·1 answer
  • PLEASE HELP, ITS DUE IN 2 MINUTES, I'LL GIVE 25 POINTS
    10·1 answer
  • If f(x) = x2 – 3, then f(-1) is equivalent<br> to
    6·2 answers
  • In which of the following do you expect the correlation coefficient to be negative?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!