# Calculus

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A stone is dropped from the upper observation deck of a tower, 200 m above the ground. (Assume g = 9.8 m/s^2.)

a)Find the distance (in meters) of the stone above ground level at time t.

b)With what velocity does it strike the ground? (Round your answer to one decimal place.)

c)If the stone is thrown downward with a speed of 2 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

• Calculus -

a = -g = -9.8
v = vi + a t = 0 -9.8 t
h = hi+vi t +.5 a t^2 = 200 +0- 4.9 t^2

there is an easy way to find v at ground using energy but this is calculus, not physics so:

0 = 200 - 4.9 t^2
t = 6.39 seconds to hit
v = 0 - 9.8 (.39 )
= -62.6 or 62.6 meters/second down

now if vi = -2
0 = 200 - 2t - 4.9 t^2
4.9 t^2 + 2 t - 200 = 0

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