A train moving near the speed of light enters a tunnel. According to a person standing in the middle of the tunnel, the back end
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Answer: 108.81 cm and 48.66 cm
Explanation:
In this, we have to make sure to keep in mind the Gravity effects on the drops. The drops will accelerate when they fall making them travel faster. This means, the velocity is not constant.
What is know:
Height (h) = 193 cm
Gravity (g) = 981
Initial Velocity = 0
First, we can know how long it take to the drop to travel to the floor. It can be done with the following equation:
(1)
Where:
x is the distance which is 193cm
Vo is the Initial Velocity which is zero
t is the time the time it takes the drop to travel from the shower to the floor
a is the aceleration, which in this case is the gravity.
With the Initial Velocity equals zero the equations simply:
To search for the time:
t = 0.627 s
This is the time it takes a drop to fall to the floor, with this time and knowing other 3 drops have driped from the shower by this time. We can calculate how much time it takes the shower to drip each drop.
Time for Drip = t/4
Time for Drip = 0.156
This time is the difference between each drop, using the same equation we can calculate where was each drop, because now it is know how much time had each drop after being drip from the shower.
Our first is already on the floor (193 cm) with 0.627 s, The second drops have been falling for (0.627s - 0.156) 0.471 s and our third drop for (0.627s - 0.156 - 0.156) 0.315 s
We can use (1) to know how far have each drop traveled on these times. We know the Initials Velocity are 0, know we need ot know the distances.
For the second drop:
For the third drop: