If a steel ball is tossed from the top of the Berj Khalifa in Dubai, the tallest

Question

If a steel ball is tossed from the top of the Berj Khalifa in Dubai, the tallest building in the world, its height above the ground t seconds after it is dropped will be

s(t) = 2717 -16t2

feet (neglecting air resistance).

(a) How long will it take to reach the ground? [Hint: Find when the height equals zero.] (Round your answer to two decimal places.)
s

(b) Use your answer to part (a) to find the velocity with which it will strike the ground. (This is called the impact velocity. Round your answer to two decimal places.)
ft/s

(c) Find the acceleration at any time t. (This number is called the acceleration due to gravity.)
ft/s2

Explanation / Answer

s(t) = 2717-16t2

a . s=0

2717-16t2 =0

t2 = 2717/16

t = 13.03sec

b . velocity , s '(t) = -32t

At t=13.03 sec

Velocity = -32(13.03) = -416.96ft/sec

c . acceleration, s ''(t) = -32 ft/sec2

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