SOLUTION: A football is kicked into the air. The height of the football is modelled by h(t)=-5t^2+16t+1 when the height is in metres and t is the time in seconds from its release. When will

Algebra ->  Systems-of-equations -> SOLUTION: A football is kicked into the air. The height of the football is modelled by h(t)=-5t^2+16t+1 when the height is in metres and t is the time in seconds from its release. When will       Log On


   

Question 1028630: A football is kicked into the air. The height of the football is modelled by h(t)=-5t^2+16t+1 when the height is in metres and t is the time in seconds from its release. When will the football first reach the height of 13 metres?
Found 2 solutions by josmiceli, Natolino1983:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given that +h%28t%29+=+13+ where
+h%28t%29+=+-5t%5E2+%2B+16t+%2B+1+
+-5t%5E2+%2B+16t+%2B+1+=+13+
+-5t%5E2+%2B+16t+-+12+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-5+
+b+=+16+
+c+=+-12+
+t+=+%28+-16+%2B-+sqrt%28+16%5E2+-+4%2A%28-5%29%2A%28-12%29+%29%29+%2F+%282%2A%28-5%29+%29+
+t+=+%28+-16+%2B-+sqrt%28+256+-+240+%29%29+%2F+%28-10+%29+
+t+=+%28+-16+%2B-+sqrt%28+16+%29%29+%2F+%28-10+%29+
+t+=+%28+-16+%2B+4+%29+%2F+%28-10%29+
+t+=+%28-12%29%2F%28-10%29+
+t+=+1.2+
and also
+t+=+%28+-16+-+4+%29+%2F+%28-10%29+
+t+=+%28-20%29%2F%28-10%29+
+t+=+2+
----------
The first time the height of the ball is at 13 m
is 1.2 sec
-------------
check:
Here's the plot:
+graph%28+600%2C+600%2C+-2%2C+4%2C+-2%2C+15%2C+-5x%5E2+%2B+16x+%2B+1+%29+

Answer by Natolino1983(23) About Me  (Show Source):
You can put this solution on YOUR website!
H(t) = -5×t^2 +16×t + 1 = 13, where t>=0
5×t^2 -16×t + 12 =0

t= (16 +/- sqrt (16^2 -4×5×12))/(2×5)
t= (16+/-4)/10
t= 2 (s) or t = 1,2 (s)
So the minimum(first reach) time is 1,2 (s) after the kick.