Question 252842
A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below.
(a) When will the missile hit the ground?
(b) When will the missile be 1000 feet above the ground?
h=300+500t-16t^2
.
Reordering:
h=300+500t-16t^2
h=-16t^2+500t+300
(a) When will the missile hit the ground?
Set h to 0 and solve for t:
h=-16t^2+500t+300
0=-16t^2+500t+300
0=-4t^2+125t+75
Applying the quadratic equation we get:
t = {-0.59, 31.84}
The negative solution doesn't make sense -- so, throw it out leaving us with:
t = 31.98 seconds
.
(b) When will the missile be 1000 feet above the ground?
set h = 1000 and solve for t:
h=-16t^2+500t+300
1000=-16t^2+500t+300
0=-16t^2+500t-700
0=-4t^2+125t-175
Applying the quadratic equation we get:
t = {1.47 secs, 29.78 secs}
The first time is on the way up
and the second time is on the way down.