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Anni [7]
2 years ago
6

Two teams of movers are lowering a piano from the window of a 10 floor apartment building. The rope breaks when the piano is 30

meters above the ground. The movers on the ground, alerted by the shouts of the movers above, first notice the piano when it is 14 meters above the ground. How long do they have to get out of the way before the piano hits the ground
Mathematics
1 answer:
GuDViN [60]2 years ago
4 0

By solving the motion equations for the piano, we will see that they have 0.7 seconds to react.

<h3>How to find the motion equation for the piano.</h3>

So the piano is in a free fall from a height of 30m.

The motion equations will be given by:

  • The only force acting on the piano will be the gravitational one, thus the acceleration of the piano is the gravitational acceleration: a(t) = -9.8m/s^2 (Where the negative sign is because it is falling down).
  • To get the velocity we integrate over time, because the piano has no initial velocity, the constant of integration is zero: v(t) = (-9.8m/s^2)*t
  • To get the position equation we integrate again, here the initial position is 30 meters above the ground, so that will be our constant of integration: p(t) = (1/2)*(-9.8m/s^2)*t^2 + 30m

<h3>How long takes to fall?</h3>

We want to find the value of t such that the position is equal to zero, so we need to solve:

0 = (1/2)*(-9.8m/s^2)*t^2 + 30m

30m = (1/2)*(9.8m/s^2)*t^2

2*30m/(9.8m/s^2) = t^2

6.1 s^2 = t^2

√(6.1 s^2) = 2.5s = t

This means that the piano falls to the ground in 2.5 seconds.

But the workes notice it when the piano is 14 meters above the ground, it happens when:

p(t) = 14m =  (1/2)*(-9.8m/s^2)*t^2 + 30m

Solving that we get:

30m - 14m =  (1/2)*(9.8m/s^2)*t^2

2*16m/(9.8m/s^2) = t^2

3.27s^2 = t^2

√(3.27s^2) = t = 1.8s

So the piano falls in 2.5 seconds, and the works notice it 1.8 seconds after it starts falling, meaning that they have:

2.5 - 1.8 = 0.7 seconds to react.

If you want to learn more about motion equations, you can read:

brainly.com/question/2473092

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Aleksandr [31]

Answer:

-5

Step-by-step explanation:

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5 0
3 years ago
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A tiger can eat up to 55 pounds a meat a day about hiw many days would it take to eat the follwing pray
Sholpan [36]
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4 0
3 years ago
PLEASE HELPPPP!!!!!!!
Strike441 [17]

Answer:

Subtract 4 from each side

Step-by-step explanation:

x + 4 > -8

Subtract 4 from each side

x + 4-4 > -8-4

x>-12

6 0
2 years ago
What is the domain of <br> F(x)=√x ?<br><br> (PLEASE HELP ASAP)
leva [86]

Option C. all real numbers greater than 0 is the correct answer

Further explanation:

Domain is the set of all inputs on which the function is defined or real.

The given function is:

f(x)=\sqrt{x}

As the function involves a square root, we have to avoid negative numbers.

  • All positive real numbers will produce defined output so the positive real numbers will be included in the domain.
  • If we look at negative real numbers, we will be taking square root of a negative number which will not result in a real number

So the domain will only include positive real numbers.

Hence, Option C. all real numbers greater than 0 is the correct answer.

Keywords: Domain, Domain of radical functions

Learn more about domain at:

  • brainly.com/question/3511750
  • brainly.com/question/3852778

#LearnwithBrainly

5 0
3 years ago
Match the average rates of change of f(x) to the corresponding intervals.
spin [16.1K]

The average rates of change of f(x) and their corresponding intervals are given as:

Interval          Rate of Change

[-5, -1]                 -8

[-4, -1]                 -7

[-3, 1]                  -4

[-2, 1]                  -3.

<h3>What is the explanation for the above?
</h3>

Step 1 - See Table Attached

Step 2 - State the formula for rate of change

The formula for rate of change is given as:
= [change in f(x)] / [change in x]

a) For interval [5, -1] ⇒

Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]  

= [-1 - 35] / [-1+5]

= -36 / 4

= - 8

b) For interval [-4, -1] ⇒

rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]

= [3 - 24] / [-1 + 4]

= -21/3

= - 7

c) interval [-3,1] ⇒

rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]

= [-1 - 15] / [1 + 3]

= -16/4

= - 4

d) interval [-2,1] ⇒

rate of change = [f (1) - f(-2)] / [1 - (-2)]

= [ -1 - 8] / [1 + 2]

= -9/3

= -3

Learn more about rate of change at:
brainly.com/question/25184007
#SPJ1

Download xlsx
6 0
2 years ago
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