Question

Can someone please help me solve this....D=

A stone is thrown straight down from the edge of a roof, 725 ft above the ground, at a speed of 7 ft/sec.

A. Given that the acceleration due to gravity is -32 ft/sec2, how high is the stone 4 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

write down all teh info u have is the best idea :)

s= 725ft
u= 7ft/s
a=32/ft/s
since that initial velocity is also acting downward, the gravity can also change to positive value.

when t=4
\[s=ut + 1/2 at\]\[s=7ft/s+1/2(32ft/s²)(16s²)=263ft\]
that is only the distance it travelled, actual height is :
725ft-263ft=462ft.


to find its velocity after 4 second:
\[v=u+at=7ft/s+32ft/s² \times 4s=135ft/s\]
this velocity will be used as initial velocity in next calculation


now:
s=465ft
u=135ft/s
a=32ft/s²

final velocity:
\[v²=u² + 2as\]\[v=\sqrt{(135ft/s)²+2 \times 32ft/s² \times t}=218.616ft/s\]

and with the final velocity,v we can use this equation:
\[s=1/2(u+v)t\]\[462ft=1/2(135ft/s+218.161ft/s)t\]\[(462ft \times 2)/353.616ft/s=t=2.613\]
2.613 is the time fort the stone to reach the ground after 4 second, therefore, u need to plus 4 second back, and the total time for the whole free falling is 6.613s

Answer 2

Hey, this is jst a correction on hei's answer
from s = ut + 1/2 at2; then
s = (7*4) +(1/2 *32*16)
=28 +256
=284ft
actual height = 725 - 284
= 441ft

Answer 3

all the 263 need to change to 284
and 462 change to 441
2.613s change to 2.494s
total time taken change to 6.494s,
thanks for the correction :)