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If a stone falls from rest and takes 16 seconds to hit the ground How tall is the ledge?
The use of more accurate figures for gravity (a) will affect the answer, as does the figure of 16 seconds which limits the significant figures of the answer.
For a = 9.8 m/sec2, the result is 1.3 x 103 meters.
For a = 9.80665 m/sec2, the result is 1255.2512 meters.
First Calculation
Using the equation
s = ut +1/2at2
Where s = displacement, u = initial velocity, a = acceleration & t = time.
Since
u = 0, t = 16s & a = 9.80665 ms2
s = (0 * 16) + (1/2 * 9.8 * 162)
s = 0 + 1255.2512
s = 1255.2512 meters
Second Calculation
First, we must assume that there is negligible air resistance. This is questionable because by analysis, one can see that the stone will be traveling quickly by the time it approaches the ground. However, it is necessary because we do not know any of the characteristics of the stone (dimensions/mass), nor the fluid resistance constant of the air.
Using a common kinematics formula, it is them possible to find the height of the ledge. Note that since the stone falls (rather than being thrown, or the like) it has an initial velocity of zero. The acceleration due to gravity used is 9.8m/s2. A rounded version of the constant is used because the question does not state whereabouts this ledge is, and acceleration due to gravity changes slightly based on where one is.
d=Vit+(1/2)*at2
d=0+(1/2)*(9.8m/s2)(16s)2
d=1254.4m
Considering significant figures, the height of the ledge is 1.2x103m.
Third Calculation
Assuming that air resistance is negligible, the ledge is 1254.4 meters tall.
Use the kinematics equation x = 0.5at2 + v0t + x0
where a stands for acceleration, t for time, v0 for initial velocity, and x0 for initial position.
We are given that v0 = 0. We can also say that the top of the ledge is x0 and that x0 = 0. Furthermore since we assumed that the only force acting on the stone is gravity, gravity is the force that will provide the acceleration. Thus, a = g = 9.8m/s2.
Putting this all together we get x = 0.5(9. 8m/s2)(16 sec)2 + (0)(16 sec) + 0 = 1254.4 m.
Note that if you are using significant figures the answer will be 1.3 x 103 m.
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