Well, there you have a very important principle wrapped up in that question.
There's actually no such thing as a real, actual amount of potential energy.
There's only potential <em><u>relative to some place</u></em>. It's the work you have to do
to lift the object from that reference place to wherever it is now. It's also
the kinetic energy the object would have if it fell down to the reference place
from where it is now.
Here's the formula for potential energy: PE = (mass) x (gravity) x (<em><u>height</u></em><u>)</u> .
So naturally, when you use that formula, you need to decide "height above what ?"
If you're reading a book while you're flying in a passenger jet, the book's PE is
(M x G x 0 meters) relative to your lap, (M x G x 1 meter) relative to the floor of the
plane, (M x G x 10,000 meters) relative to the ground, and maybe (M x G x 25,000 meters)
relative to the bottom of the ocean.
Let's say that gravity is 9.8 m/s² .
Then a 4kg block sitting on the floor has (39.2 x 0 meters) PE relative to the floor
it's sitting on, also (39.2 x 3 meters) relative to the floor that's one floor downstairs,
also (39.2 x 30 meters) relative to 10 floors downstairs, and if it's on the top floor of
the Amoco/Aon Center in Chicago, maybe (39.2 x 345 meters) relative to the floor
in the coffee shop that's off the lobby on the ground floor.
<span>a) 1960 m
b) 960 m
Assumptions.
1. Ignore air resistance.
2. Gravity is 9.80 m/s^2
For the situation where the balloon was stationary, the equation for the distance the bottle fell is
d = 1/2 AT^2
d = 1/2 9.80 m/s^2 (20s)^2
d = 4.9 m/s^2 * 400 s^2
d = 4.9 * 400 m
d = 1960 m
For situation b, the equation is quite similar except we need to account for the initial velocity of the bottle. We can either assume that the acceleration for gravity is negative, or that the initial velocity is negative. We just need to make certain that the two effects (falling due to acceleration from gravity) and (climbing due to initial acceleration) counteract each other. So the formula becomes
d = 1/2 9.80 m/s^2 (20s)^2 - 50 m/s * T
d = 1/2 9.80 m/s^2 (20s)^2 - 50m/s *20s
d = 4.9 m/s^2 * 400 s^2 - 1000 m
d = 4.9 * 400 m - 1000 m
d = 1960 m - 1000 m
d = 960 m</span>
A! Good luck on your test!
The first person = A
The second one = B
velocity of A = 3 km / h
velocity of B = 4 km / h
Distance of A = 3t
Distance of B = 35 - 4t
At what time do they meet?
3t = 35 - 4t
7t = 35
t = 5 hours
7 a.m. + 5 hours = 12 p.m.
(2.00 hours) x (3,600 seconds/hour) = 7,200 seconds
(9.00 minutes) x (60 seconds/minute) = 540 seconds
The record time = (7,200 + 540 + 21) = 7,761 seconds
Distance = (speed) x (time)
= (5.436 m/s) x (7,761 sec) =<span> 42,188.8 meters
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The official length of the marathon run is 42,195 meters.
If we divide that by the record time in the question, we get
5.4368... m/s .
Rounded to the nearest thousandth, that's 5.437 m/s.
If the question had given the speed as 5.437 instead of 5.436 ,
then we would have calculated the distance to be
(5.437 m/s) x (7,761 sec) =<span> 42,196.6 meters,
4.6 meters closer to the official distance than the answer we did get.
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