Question 1128492
<font color="black" face="times" size="3">
Part A)


v = initial velocity = 0
s = 500 = vertical distance the object travels (from plane to ground)


Plug in the given values and solve for t
4.9t^2 + v*t = s
4.9t^2 + 0*t = 500
4.9t^2 + 0 = 500
4.9t^2 = 500
t^2 = 500/4.9
t^2 = 102.04081632653
t = sqrt(102.04081632653)
t = 10.101525445522
t = 10.1015


--------------------


Answer: 10.1015 seconds (this is approximate)


=======================================================
Part B)


v = 10 
s = 500
like in part A, the goal is to solve for t


First plug in the values and get everything to one side
4.9t^2 + v*t = s
4.9t^2 + 10*t = 500
4.9t^2 + 10*t - 500 = 0


Then use the Quadratic Formula with a = 4.9, b = 10, c = -500
{{{t = (-b+sqrt(b^2-4ac))/(2a)}}} or {{{t = (-b-sqrt(b^2-4ac))/(2a)}}}
{{{t = (-10+sqrt((10)^2-4(4.9)(-500)))/(2(4.9))}}} or {{{t = (-10-sqrt((10)^2-4(4.9)(-500)))/(2(4.9))}}}
{{{t = (-10+sqrt(9900))/(9.8)}}} or {{{t = (-10-sqrt(9900))/(9.8)}}}
{{{t = (-10+99.498743710662)/(9.8)}}} or {{{t = (-10-99.498743710662)/(9.8)}}}
{{{t = (89.498743710662)/(9.8)}}} or {{{t = (-109.498743710662)/(9.8)}}}
{{{t = 9.1325248684349}}} or {{{t = -11.1733411949655}}}


Toss out the negative t value (negative time values make no sense)


--------------------


Answer: 9.1325 seconds (approximate)


=======================================================
Part C)


v = 10
t = 8
s = unknown


Plug in the given values and compute
4.9t^2 + v*t = s
s = 4.9t^2 + v*t
s = 4.9*8^2 + 500*8
s = 4.9*64 + 500*8
s = 313.6 + 4000
s = 4313.6


--------------------


Answer: 4313.6 feet
</font>