SOLUTION: An object is projected directly upward from the ground. After t seconds its distance in feet above the ground is given by h(t) = -16t^2 + 160t. a. How high is the projectile af

Algebra ->  Human-and-algebraic-language -> SOLUTION: An object is projected directly upward from the ground. After t seconds its distance in feet above the ground is given by h(t) = -16t^2 + 160t. a. How high is the projectile af      Log On


   

Question 1114773: An object is projected directly upward from the ground. After t seconds its distance in feet
above the ground is given by h(t) = -16t^2 + 160t.
a. How high is the projectile after 5 seconds?
b. At what time(s) is the projectile 110 feet from the ground?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
h%28t%29+=+-16t%5E2+%2B+160t
a. How high is the projectile after t=5+seconds?
h%28t%29+=+-16t%5E2+%2B+160t....plug in 5 for t
h%285%29+=+-16%285%29%5E2+%2B+160%2A5
h%285%29+=+-16%2A25+%2B+160%2A5
h%285%29+=+-400+%2B+800
h%285%29+=+400+ feet from the ground

b. At what time(s) is the projectile h=110 feet from the ground?
h%28t%29+=+-16t%5E2+%2B+160t....plug in 110 for h
110+=+-16t%5E2+%2B+160t...solve for t
16t%5E2-160t%2B110+=+0+....use quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-160%29+%2B-+sqrt%28+%28-160%29%5E2-4%2A16%2A110+%29%29%2F%282%2A16%29+
t+=+%28160+%2B-+sqrt%28+25600+-7040+%29%29%2F32+
t+=+%28160+%2B-+sqrt%28+18560+%29%29%2F32+
t+=+%28160+%2B-+136.23509%29%2F32+
t+=+%28160%2F32+%2B-+136.23509%2F32%29+
t+=+%285+%2B-+4.2575%29+
t+=+9.26 seconds
and
t+=+0.74 seconds