Question 1072666: Peter is standing on a bridge and throws a stone up into the air at 30 m/s. The stone hits the surface of the water below 10 seconds later. From what height above the surface of the water did Peter throw the stone? (Note: the acceleration due to gravity is 10 m/s^2 )
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! WITHOUT FORMULAS:
The initial upwards speed was  .
For  , that upwards speed decreased linearly due to gravity
by  each       ,
for a total decrease of   
to  .
The average upwards speed for those was
  .
At an average speed of  for ,
the stone's upwards displacement was
 
So, the stone left Peter's hand  above the surface of the water.
WITH FORMULAS:
You may have learned in physics class that, for an object moving linearly under constant acceleration,
its position  as a function of time  can be modeled as
 , where
 is the constant acceleration, while
 and  are respectively the position and velocity of the object at  .
You could choose to measure position as height (in meters) above the water surface,
and time (in seconds) since the stone left Peter's hand.
In that case, distance above the water, upwards velocity and upwards acceleration are positive,
so initial velocity is   ,
acceleration is   ,
is what you are looking for ,
and you know that  at  .
Substituting into  ,
 ,
 ,
 , and  (in meters , of course).
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