If a stone is dropped from a height of 1024 feet its height

If a stone is dropped from a height of 1,024 feet, its height s after t seconds is given by s(t) = 1,024 - 16t^2, with s in feet.

(a) Compute s\'(t)

s \' (t) = ________

(b) when does it reach the ground, and how fast is it traveling when it hits the ground? (hint, it reahes the ground when s(t)=0)

The stone is traveling at a velocity of ____ ft/sec when it hits the ground at ___ seconds

Solution

s(t)= 1024-16t²

s\'(t) = 0-2*16t=-32t ft/sec

b. s(t)=0

1024-16t²=0

16t²=1024

t²=64

t=8

s\'(8)= -32*8=-256ft/sec

The stone is travelling at a velocity of 256 ft/sec when it hits the ground at 8secs.