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
