SOLUTION: Wile E. Coyote is standing on a springboard atop a high cliff. Roadrunner drops a boulder on the other end of the springboard, sending Wile up with an initial velocity of 4ft/sec.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Wile E. Coyote is standing on a springboard atop a high cliff. Roadrunner drops a boulder on the other end of the springboard, sending Wile up with an initial velocity of 4ft/sec.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 763222: Wile E. Coyote is standing on a springboard atop a high cliff. Roadrunner drops a boulder on the other end of the springboard, sending Wile up with an initial velocity of 4ft/sec. At what time will he land in the river, 120 feet below the cliff? (h=-16t^2+VoT+S where Vo is the initial velocity, s is the initial height, and t is time)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
W.E.C. will land in the riven when +h+=+0+
when his height is zero
+v%5B0%5D+=+4+ ft/sec
+s+=+120+
+h%28t%29+=+-16t%5E2+%2B+v%5B0%5D%2At+%2B+s+
+0+=+-16t%5E2+%2B+4t+%2B+120+
+0+=+-4t%5E2+%2B+t+%2B+30+
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-4+
+b+=+4+
+c+=+30++
+t+=+%28+-1+%2B-+sqrt%28+1%5E2+-+4%2A%28-4%29%2A30+%29%29+%2F+%282%2A%28-4%29%29+
+t+=+%28+-1+%2B-+sqrt%28+1+%2B+480+%29%29+%2F+%28-8%29+
+t+=+%28+-1+-+sqrt%28+481+%29%29+%2F+%28-8%29+
+t+=+%28+-1+-+21.932%29+%2F+%28-8%29+
+t+=+-22.932+%2F+%28+-8+%29+=+2.866+
In 2.866 sec, he lands in the river
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+4%2C+-20%2C+140%2C+-16x%5E2+%2B+4x+%2B+120+%29+
The time at +h+=+0+ looks about right