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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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She was riding for 2 hours and 30 mins
8 0
3 years ago
How to solve this?? (-4)-(-8)+(-4)
kirill115 [55]
(-4) - (- 8) + (- 4)
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6 0
2 years ago
Read 2 more answers
Plz answer both questions 15 points
anyanavicka [17]

Answer:

If the signs of rational numbers are same, then the answer is positive.

If the signs of rational numbers are different, then the answer is negative.

Step-by-step explanation:

Consider the provided information.

A: When multiplying or dividing rational numbers, when will the answer be positive?

If we are multiplying or dividing rational numbers the answer will be positive if and only if both the rational numbers have same sign.

For example: Multiply 2 and 4.

2×4=8              (same sign)

or

Multiply -2 and -4.

-2×-4=8         (same sign)

8 is a positive rational number.

Now divided 2 and 4.

\frac{2}{4} =\frac{1}{2}    

or

Divided -2 and -4.

\frac{-2}{-4} =\frac{1}{2}

1/2 is a positive rational number.

Hence, If the signs of rational numbers are same, then the answer is positive.

B: When multiplying or dividing rational numbers, when will the answer be negative?

If we are multiplying or dividing rational numbers the answer will be negative if and only if both the rational numbers have different sign.

For example: Multiply 2 and -4.

2×-4=-8              (different sign)

or

Multiply -2 and 4.

-2×4=-8             (different sign)

-8 is a negative rational number.

Now divided 2 and -4.

\frac{2}{-4} =-\frac{1}{2}

or

Divided -2 and 4.

\frac{-2}{4} =-\frac{1}{2}

-1/2 is a negative rational number

Hence,  If the signs of rational numbers are different, then the answer is negative.

3 0
2 years ago
A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 11 units. Find the measure of the longer diag
lord [1]

The measure of the longer diagonal is 24.31 units

<h3>How to determine the longer diagonal?</h3>

The side lengths are given as;

a = 16

b = 10

The shorter diagonal is represented as d1, and it is given as

d1 = 11

The longer diagonal is represented as d2, and it is calculated using

d1^2 + d2^2 = 2 * (a^2 + b^2)

Substitute the known values in the above equation

11^2 + d2^2 = 2 * (16^2 + 10^2)

Evaluate the sum

121 + d2^2 =2 * 356

Evaluate the product

121 + d2^2 = 712

Subtract 121 from both sides

d2^2 = 591

Take the square root of both sides

d2 = 24.31

Hence, the measure of the longer diagonal is 24.31 units

Read more about parallelograms at:

brainly.com/question/970600

#SPJ1

4 0
1 year ago
HELP ASAP I WILL GIVE BRAINLIST
VikaD [51]

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2\pir             ( Calculate the total circumference)    

C = 2(8)\pi

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

6 0
3 years ago
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