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 ste 1,024-162, with s in feet. (a) Compute ste). sYc)- 0, 1, 2, 3, and 4 seconds. ft/sec t/sec ftysec ft/sec ft/sec Find its velocity at times t s12) (b) when does it reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) 0.1 The stone is traveling at a velocity of ft/sec when it hits the ground at seconds Need Help? asdTalk to

Solution

s(t)= 1024-16t²

a. s\'(t)= 0- 2*16 t= -32t

b. s\'(0)=-32(0)=0 ft/sec

s\'(1)= -32(1) =-32 ft/sec

s\'(2)= -32(2) =-64 ft/sec

s\'(3)= -32(3)=-96 ft/sec

s\'(4)=-32(4) =-128ft/sec

c. The stone reach the ground when s(t)=0

1024 -16t²=0

1024=16t²

t²=64

t= 8 sec

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