SOLUTION: The height h (in meters) of a cannonball t seconds after it is fired from a cannon is described by the equation h(t)=-49t^2+60t. a. What is the height of the cannonball after 4

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Question 624215: The height h (in meters) of a cannonball t seconds after it is fired from a cannon is described by the equation h(t)=-49t^2+60t.
a. What is the height of the cannonball after 4 seconds?
b. How long will the cannonball be in the air?
c. How long does it take the cannonball to reach its maximum height?
d. What is the maximum height of the cannonball?

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
The height h (in meters) of a cannonball t seconds after it is fired from a cannon is described by the equation
h(t)=-49t^2+60t.
a. What is the height of the cannonball after 4 seconds? h(4) = -544m
b. How long will the cannonball be in the air? 1.22 sec
0 = -49t^2 + 60t = t(-49t + 60)
49t= 60
t = 60/49 = 1.22 sec
Completing Square: y = ax^2 + bx + c ⇒ y = a(x -(-b/a2)^2 - a(-b/2a)^2 + c
h%28t%29=-49%28t-60%2F98%29%5E2+%2B+49%2860%2F98%29%5E2 , V(60/98, 18.3673)
the vertex form of a Parabola opening up(a>0) or down(a<0), y=a%28x-h%29%5E2+%2Bk
where(h,k) is the vertex and the Line of symmetry is x = h
c. How long does it take the cannonball to reach its maximum height? 60/98 sec
d. What is the maximum height of the cannonball? 18.3673m