An object is dropped from a tower, 154 ft above the ground. The object\'s height

Question

An object is dropped from a tower, 154 ft above the ground. The object's height above ground t sec into the fall is s= 154 - 16t^2. What is the object's velocity, speed, and acceleration at time t? About how long does it take the object to hit the ground? What is the object's velocity at the moment of impact? The object's velocity at time t is The object's speed at time t is ft/sec. The object's acceleration at time t is ft/sec^2. (Simplify your answer.) It takes sec for the object to hit the ground. (Round to the nearest tenth.) The object's velocity at the moment of impact is ft/sec. (Round to the nearest tenth.)

Explanation / Answer

given s=154-16t2

a) velocity =ds/dt =-32t

speed =|ds/dt|=32t ft/sec

acceleration =d2s/dt2=-32 ft/sec2

at ground s =0

154-16t2=0

t2=154/16

t=3.1 sec

it takes 3.1sec for the object to hit the ground

velocity at the moment of impact =-32*3.1

velocity at the moment of impact =-99.2ft/sec

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