SOLUTION: please can you help mw with this question: a ball is dropped from a tall building and falls from acceleration of magnitude 10ms-2. the distance between floors in the block is co

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please can you help mw with this question: a ball is dropped from a tall building and falls from acceleration of magnitude 10ms-2. the distance between floors in the block is co      Log On


   

Question 825784: please can you help mw with this question:
a ball is dropped from a tall building and falls from acceleration of magnitude
10ms-2. the distance between floors in the block is constant. the ball take 0.5s to fall from the 14th to the 13th floor and 0.3 s to fall from the 13th floor to the 13th. what is the distance between floors?
thankyou
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
d= constant distance between floors, in meters
g=10m%22%2F%22s%5E2= acceleration of gravity
v= downward velocity as the ball reaches the 14th floor, in m/s
Then, 0.5 seconds later, we have
v%2B10%2A0.5=v%2B5= downward velocity as the ball reaches the 13th floor.
After another 0.3 seconds,
v%2B10%2A0.5%2B10%2A0.3=v%2B8= downward velocity as the ball reaches the 12th floor.
In linear motion with constant acceleration, distance is the product of average speed and time.
Between the 14th and 13th floors:
%28%28v%2B%28v%2B5%29%29%2F2%29%2A0.5=d
%282v%2B5%29%2F2=2d
highlight%282v%2B5=4d%29
Between the 13th and 12th floors:
%28%28v%2B8%29%2B%28v%2B5%29%29%2F2%29%2A0.3=d
%28%28v%2B8%29%2B%28v%2B5%29%29%2F2%29%2A3=10d
%28%28v%2B8%29%2B%28v%2B5%29%29%2A3=20d
%282v%2B13%29%2A3=20d
highlight%286v%2B39=20d%29

We solve the system below any way we can
system%282v%2B5=4d%2C6v%2B39=20d%29 --> system%28v=3.5%2Chighlight%28d=3%29%29 to find that the distance between floor is highlight%283%29meters.

I would use a combination of equations:
2v%2B5=4d-->3%282v%2B5%29=3%2A%284d%29-->6v%2B15=12d
6v%2B39=20d
-
6v%2B15=12d
-----------
24=8d --> 24%2F8=d --> highlight%28d=3%29