Calculus Question

Question

A stone is thrown straight down from the edge of a roof, 1125 ft above the ground, at a speed of 5 ft/sec.

A. Given that the acceleration due to gravity is -32 ft/sec2, how high is the stone 5 seconds later?  ft.

B. At what time does the stone hit the ground?  sec.

C. What is the velocity of the stone when it hits the ground?  ft/sec.

Answer 1

h=-16t^2+5t+1125

h(5)= -16(25)+5(5)+1125= 750 feet after 5 seconds

-16t^2+5t+1125=0

t= 5/32+(1/32)sqr(25+64(1125)

=about (5+268.3747)/32

= 8.543 seconds to hit the ground

v=h'=-32t+5

v(8.532)= -32(8.532)+5= about -268.37 feet/sec = velocity when it hits the ground