A stone is dropped from the roof of a tall building. A person measures the speed of the stone to be 49 m/s when it hits the ground. What is the height of the building?
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vfinal^2=VI+2g*h solve for h
To find the height of the building, we need to use the equation of motion for an object in free fall:
v² = u² + 2as
Where:
v = final velocity (49 m/s in this case)
u = initial velocity (0 m/s as the stone is dropped)
a = acceleration due to gravity (-9.8 m/s², assuming downward as positive)
s = displacement (height of the building)
Plugging in the values:
49² = 0² + 2(-9.8)s
2401 = -19.6s
Divide both sides of the equation by -19.6:
s = 2401 / -19.6
s ≈ -122.56
Since height cannot be negative, we can take the absolute value:
s ≈ 122.56 m
Therefore, the height of the building is approximately 122.56 meters.
To find the height of the building, we can use the equation of motion for an object in free fall:
h = (1/2)gt^2
Where:
h is the height of the building,
g is the acceleration due to gravity (~9.8 m/s^2),
and t is the time it takes for the stone to hit the ground.
To find the time it takes for the stone to hit the ground, we can use the equation for velocity:
v = gt
where:
v is the final velocity of the stone (49 m/s),
g is the acceleration due to gravity (~9.8 m/s^2),
and t is the time taken.
Rearranging this equation, we have:
t = v / g
Substituting the given values:
t = 49 m/s / 9.8 m/s^2 = 5 seconds
Now that we know the time, we can find the height of the building by substituting the time into the original equation:
h = (1/2)gt^2 = (1/2)(9.8 m/s^2)(5 s)^2 = 122.5 m
Therefore, the height of the building is approximately 122.5 meters.