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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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Find x and y. <br><br> pls pls help
Anna [14]

Answer:

x = 65 , y = 64

Step-by-step explanation:

y - 16 and 2y + 4 are same- side interior angles and sum to 180° , that is

y - 16 + 2y + 4 = 180

3y - 12 = 180 ( add 12 to both sides )

3y = 192 ( divide both sides by 3 )

y = 64

then

2y + 4 = 2(64) + 4 = 128 + 4 = 132

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

2y + 4 is an exterior angle of the triangle , then

x + 67 = 132 ( subtract 67 from both sides )

x = 65

7 0
1 year ago
Help please i really really really need it.....
ruslelena [56]

A)

s = sweater

j = jeans

Equations:

4s + 2j = 140

2s + 3j = 150

B)

4s + 2j = 140

2s + 3j = 150

Multiply (-2) to the second equation

-2 (2s + 3j = 150)

-4s - 6j = -300

Now you have the equations:

4s + 2j = 140

-4s - 6j = -300

-----------------------------add

-4j = -160

  j = 40

4s + 2(40) = 140

4s + 80 = 140

4s = 60

 s = 15

The cost for a sweater is $15 and the cost for a jean is $40

We used the elimination method to solve the system of equations.

C)

Each pair of jean, she will buy 3 sweaters so total = 40 + 3(15) = $85

Total cost for 1 pair of jeans and 3 sweaters = $85

If she has $225 the

$225 / $85 = 2.64

2 jeans = 2 x 40 = $80

6 sweaters = 6 x $15 = $90

So She can only buy 2 jeans and 6 sweaters

3 0
3 years ago
A line passes through the points (2,4) and (5,6) .
Alenkinab [10]

Answer:

Option B and D are correct.

Step-by-step explanation:

Given: A line passes through the points (2,4) and (5,6).

* Case 1:

If a line passes through the points (2, 4) and (5, 6)

Point slope intercept form:

for any two points (x_1,y_1) and (x_2, y_2)

then the general form y -y_1=m(x-x_1) for linear equations where m is the slope given by:

m =\frac{y_2-y_1}{x_2-x_1}

First calculate slope for the points (2, 4) and (5, 6);

m = \frac{y_2-y_1}{x_2-x_1} =\frac{6-4}{5-2} = \frac{2}{3}

then, by point slope intercept form;

y-4=\frac{2}{3}(x-2)

* Case 2:

If a line passes through the points (5, 6) and (2, 4)

First calculate slope for the points (5, 6) and (2, 4);

m = \frac{y_2-y_1}{x_2-x_1} =\frac{4-6}{2-5} = \frac{-2}{-3}= \frac{2}{3}

then, by point slope intercept form;

y-6=\frac{2}{3}(x-5)

Yes, the only equation of line from the given options  which describes the given line are;

y-4=\frac{2}{3}(x-2)  and y-6=\frac{2}{3}(x-5)



8 0
3 years ago
Simplify the expression. -3(1+n)-6n
BabaBlast [244]

Answer:

− 3 − 9 n

Step-by-step explanation:

Simplify the expression

5 0
2 years ago
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2x + 2 = -52 whats the value of x​
Sloan [31]
You answer is -25 your welcome
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