SOLUTION: A football is kicked into the air with an initial upward velocity of 29.4 meters per seconds. Using: h(t)=-4.9t^2+29.4t a. Calculate the height after 1) 2 seconds and 2) 3 seconds

Algebra ->  Inequalities -> SOLUTION: A football is kicked into the air with an initial upward velocity of 29.4 meters per seconds. Using: h(t)=-4.9t^2+29.4t a. Calculate the height after 1) 2 seconds and 2) 3 seconds      Log On


   

Question 980034: A football is kicked into the air with an initial upward velocity of 29.4 meters per seconds. Using: h(t)=-4.9t^2+29.4t
a. Calculate the height after 1) 2 seconds and 2) 3 seconds
b. When will the ball be at its maximum height and what is the maximum height?
c. When will the ball hit the ground?
d. What is the domain and range for this function?
please help me with this summer packet question. Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-4.9t%5E2+%2B+29.4t+
(a)
+t+=+2+
+h%282%29+=+-4.9%2A2%5E2+%2B+29.4%2A2+
+h%282%29+=+-19.6+%2B+58.8+
+h%282%29+=+39.2+ m
-------------------
+t+=+3+
+h%283%29+=+-4.9%2A3%5E2+%2B+29.4%2A3+
+h%283%29+=+-44.1+%2B+88.2+
+h%283%29+=+44.1+ m
------------------
(b)
The horizontal coordinate of the max height
is at +t%5Bmax%5D+=+-b%2F%282a%29+ where
+a+=+-4.9+
+b+=+29.4+
---------------
+t%5Bmax%5D+=+-29.4+%2F+%28-9.8+%29+
+t%5Bmax%5D+=+3+ sec
------------------
The max height is at +h%283%29+=+44.1+ m
as already shown
-----------------
(c)
The ball hits the ground when +h%28t%29+=+0+
+-4.9t%5E2+%2B+29.4t++=+0+
+t%2A%28+-4.9t+%2B+29.4+%29+=+0+
+4.9t+=+29.4+
+t+=+6+
The ball hits the ground in 6 sec
------------------------------
(d)
The range is +0+ to +44.1+
The domain is +0+ to +6+
-----------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+7%2C+-5%2C+50%2C+-4.9x%5E2+%2B+29.4x+%29+