Question 1007759: With what velocity will a stone strike the ground if dropped from the top of the building 400 ft high?Solve by integration. Found 3 solutions by Fombitz, Alan3354, rothauserc:Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! Assuming there is no air resistance and gravity is equal to
When , .
So then,
When ,
Find when the stone hits the ground ,
So then the velocity is,
You can put this solution on YOUR website! With what velocity will a stone strike the ground if dropped from the top of the building 400 ft high?Solve by integration.
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h(t) = -16t^2 + vo*t + ho is commonly used with feet units (vo = initial speed, ho = initial height)
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h(t) = -16t^2 + 400
h(t) = 0 at impact
-16t^2 + 400 = 0
t = 5 seconds (Ignore the -5)
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v = a*t = 32*5
v at impact = 160 ft/sec
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There's nothing to integrate.
You can put this solution on YOUR website! dv / dt = a and integrating this we get
v = c + at where c is initial velocity, a is acceleration of gravity and t is time
in our problem c is 0 since the stone is dropped and a = 32 feet/sec^2
now distance covered is the integration of v with respect to time, so
we integrate v = at and get
distance = (1/2)at^2, therefore
400 = (1/2)* 32 * t^2
t^2 = 800 / 32
t = 5 seconds, now
v = 32 * 5 = 160 feet per second when the stone hits the ground
